Phonon-based partition of (ZnSe-like) semiconductor mixed crystals on approach to their pressure-induced structural transition

The generic 1-bond → 2-mode “percolation-type” Raman signal inherent to the short bond of common A1−xBxC semiconductor mixed crystals with zincblende (cubic) structure is exploited as a sensitive “mesoscope” to explore how various ZnSe-based systems engage their pressure-induced structural transition (to rock-salt) at the sub-macroscopic scale—with a focus on Zn1−xCdxSe. The Raman doublet, that distinguishes between the AC- and BC-like environments of the short bond, is reactive to pressure: either it closes (Zn1−xBexSe, ZnSe1−xSx) or it opens (Zn1−xCdxSe), depending on the hardening rates of the two environments under pressure. A partition of II–VI and III–V mixed crystals is accordingly outlined. Of special interest is the “closure” case, in which the system resonantly stabilizes ante transition at its “exceptional point” corresponding to a virtual decoupling, by overdamping, of the two oscillators forming the Raman doublet. At this limit, the chain-connected bonds of the short species (taken as the minor one) freeze along the chain into a rigid backbone. This reveals a capacity behind alloying to reduce the thermal conductivity as well as the thermalization rate of photo-generated electrons.


I. Zn1-xCdxSe
A. Nature of the Cd⇿Zn atom substitution in Zn0.83Cd0.17Se In a recent Raman study of Zn1-xCdxSe 19 we argued that the magnitude of the inverted − − splitting due to the minor mode situated within the main − − + band can be used as a convenient marker with two respects. It primarily helps to decide whether the ( − , − ) doublet reflects a sensitivity of the Zn-Se vibrations at the first-(large splitting) or second-neighbor (small splitting) length scale. Should neither of the two options provide reasonable agreement between experiment and theory, then additional flexibility arises by considering a deviation with respect to the ideal Cd⇿Zn substitution towards either clustering (reduction of splitting) or anticlustering (increase of splitting).
After close examination, in the above spirit, of the extended set of Zn1-xCdxSe and − frequencies carefully measured by applying far-infrared reflectivity to large size single crystals with small/moderate Cd contents (0≤x≤0.4) slightly exceeding the pure-zincblende domain (x<0.3) S1 -an overview is given in Ref. 19 (see Fig. 1 therein) -we concluded to a sensitivity of the Zn-Se vibrations extending up to second-neighbors. At least this suffices to explain the − − quasi degeneracy apparent in the reported data at small Cd content (x≤0.2). A sensitivity limited to firstneighbors would otherwise generate a finite splitting (as large as ~5 cm -1 at x=0.2) exceeding by far the experimental resolution as (~1 cm -1 ) as soon as departing from the Cd-dilute limit. Our Raman spectra lately recorded with similar single crystals at small Cd content (x=0.075, 0.170) consistently replicate the trend.
At moderate Cd-contents (0.2≤x≤0.4) the Vodopyanov's data reveal a finite − − splitting, as expected in case of a Zn-Se sensitivity at the second-neighbor scale. However, the experimental splitting remains significantly smaller than that predicted in case of an ideally random Cd⇿Zn substitution, i.e., by as much as ~50% at x~0.4. Such discrepancy was explained by considering a pronounced trend towards local clustering corresponding to a value of ~0.5 on a scale of 0 (random substitution) to 1 (local phase separation) for the order parameter introduced in Ref. 19. While such value derived at moderate Cd content is generally compatible with the observed − − quasi degeneracy throughout the composition domain, the quasi degeneracy at small Cd content is also there when considering a random substitution ( =0) -see above. It follows that the magnitude of the inverted − − splitting is not really informative regarding the nature of the Cd⇿Zn substitution at small Cd content (x<0.2), of present interest At this limit, additional insight is needed to decide.
1. Zn0.83Cd0.17Se: Nuclear magnetic resonance measurements A direct insight into the nature of the Cd⇿Zn substitution of the studied Zn0.83Cd0.17Se crystal ground as a fine powder is achieved by 77 Se solid-state nuclear magnetic resonance (NMR) measurements. The 77 Se chemical shift being sensitive to the electronic environment, it changes with the first-neighbor tetrahedral environment of the Se nucleus, out of five possible ones (from now on labeled depending on the number of Cd at the vertices, i.e., from 0 to 4, completed by Zn) in a Zn1-xCdxSe zincblende-type mixed crystal. The relative abundance of the various (0 to 4-Cd) Se-cluster units forming Zn0.83Cd0.17Se can be derived from the integrals of the related 77 Se signals, presently modeled as Gaussian functions, using the dmfit program S2 .
All NMR spectra are acquired on a Bruker Avance III 600 MHz spectrometer (14T) equipped with a Bruker 1.3 mm triple resonance MAS probe. The Y channel is not used (no insert) and the X channel is tuned to 77 Se frequency (114.42 MHz). The 1 H channel is not used, as no proton decoupling is necessary. The NMR spectra are processed by using a Gaussian apodization function with a 1000 Hz line broadening. The 77 Se chemical shift is externally calibrated using a ZnSe powder sample (containing Se-clusters of the 0-Cd type only) resonating at -350 ppm (Fig. S1a, bottom spectrum), consistently with existing measurements in the literature S3 . 77 Se 90° pulse is 2.7 s long, as determined using a Lselenomethionine powder sample (Acros Organics).
One-dimensional 77 Se spectra taken with the Zn0.83Cd0.17Se powder exhibit three distinct NMR signals at -330 ppm, -380 ppm and -430 ppm (Fig. S1a, central and top spectra). Considering the 77 Se chemical shifts of -350 ppm and -480 ppm found for ZnSe (Ref. S3) and CdSe (Ref. S4), respectively, the observed signals can be traced back to the Se-clusters of 0-, 1-and 2-Cd types, respectively -in order of increasing magnitude of the 77 Se chemical shift. A similar ordering/deshielding effect has independently been observed with Zn1-xCdxTe 30 . A further common trend between both systems is that the parent signal(s) (presently limited to ZnSe) emerge(s) within (and not outside) the spectral domain covered by the mixed crystal(s) (Zn0.83Cd0.17Se in this case).
A prerequisite in view to achieve a reliable quantitative insight into the individual Se-clusters fractions via the areas of the corresponding NMR signals is the knowledge of the longitudinal relaxation time T1. Standard T1 measurement with a saturation recovery experiment is hampered by the low sensitivity and long T1. A precise T1 measurement could not be achieved as the first non-zero spectrum in the series of saturation-recovery experiments showed at 1000 seconds. Longer recovery time is impractical, as it might have taken a week to get the full recovery. However, this result gives at least an order of magnitude for T1, further confirmed by a series of three direct acquisition experiments with variable tilt-angle (15°, 30°, 60°) and constant recycle delay (300 s) converging towards a T1 estimate of around 10000 s. A direct acquisition experiment using short pulses (15° tilt) is recorded in 90 hours ( Fig. S1a -central spectrum). The 300 s recycle delay chosen for this experiment is between 0.1 and 0.15 T1 for each signal. This ensures that the relative intensity of each signal is within 10% of the maximum possible intensity under these conditions.
Despite efforts the signal-to-noise ratio remains rather poor -even though not negligible -in our direct acquisition experiment. This motivated an alternative approach to exploit the long homogeneous transverse relaxation time (T2*) by implementing direct-acquisition Carr-Purcell-Meiboom-Gil (CPMG) experiment S5 . In this method, several spin echoes are acquired over one scan, folded and stacked together to get an increase in the signal-to-noise ratio. The spin echoes are rotorsynchronized over 128 rotor periods for a half-echo (2.56 ms) and 32 full echoes and a half were acquired for a total acquisition time of 166.4 ms. The recycle delay chosen for this experiment (10 h) was between 3T1 and 4T1 for each signal. In this way, the relative intensity of each signal is within 10% of the signal intensity after full recovery. The quantitativity of the study is not challenged by any potential difference in T2* between signals as the stacking of each echo exhibits a linear increase in the signal-to-noise ratio. Hence, each echo is of similar intensity with respect to the first one, and T2* for each signal is much longer than the total free inductance decay acquisition time. The 90 h long direct CPMG acquisition experiment gives a much better signal-to-noise ratio than the standard direct acquisition one recorded over the same total experimental time, as apparent in Fig. S1a (compare the top and central spectra).
Hence, our approach in the following analysis is to focus on the more sensitive CPMG spectrum, which is deconvoluted by using the Dmfit program S2 (red curve superimposed onto the top raw NMR spectrum in Fig. S1a). The NMR-signal integrals derived thereof lead to relative proportions of 38%, 51% and 11% for the three detected Se-clusters of 0-, 1-and 2-Cd types, respectively. A Montecarlo analysis leads to a maximal error of 1% due to the deconvolution process, which is negligible in view of the 10% error on the integrals related to the T1 estimate. The corresponding cluster fractions derived for the same system by using the -dependent Binomial Bernouilli distribution 8 are shown in Fig. S1b, for comparison. The operative -domain for Zn0.83Cd0.17Se is bound to 0 (random substitution)fortuitously corresponding to full disappearance of the minor 4-Cd type Se-cluster at 17 at.% Cd (fixing the validity limit for the current -dependent approach) -and 1 (full clustering, i.e., local phase separation) on its low and high estimate cases, respectively. In other words any deviation from the ideal Cd⇿Zn random substitution ( =0) in Zn0.83Cd0.17Se should reflect a trend towards local clustering ( >0); anticlustering ( <0) is forbidden in principle. However, this is only theoretical, and valid provided the Cd vs. Zn arrangement in Zn0.83Cd0.17Se actually fits into the general -dependent substitution process formalized in Ref. 8.
The experimental Se-cluster (of 0-, 1-and 2-type) distribution measured from the CPMG spectrum is somehow disconcerting in that it doesn't match any theoretical -dependent Bernouilli distribution in Fig. S1b, whichever value is considered -even negative ones (in Fig. S1b, the -domain is artificially expanded to the slightly negative -value corresponding to disappearance of the next minor Se-cluster species, i.e., of 3-Cd type, to get at least a minor insight into the effect of anticlustering on the Secluster fractions of Zn0.83Cd0.17Se). In fact, the significantly larger representation of the Se-cluster of 1-Cd type with respect to the 0-Cd one points towards anticlustering ( <0). However, in this case, the development of the Se-cluster of 2-Cd type should be favored as well. This contradicts the CPMG experimental findings revealing, in fact, a sub-representation of the 2-Cd Se-cluster type with respect to the random case ( =0), as expected in case of local clustering ( >0). We conclude that the Cd⇿Zn substitution process in the current Zn0.83Cd0.17Se crystal cannot be grasped within the -dependent scheme 8 .
On this basis we re-examine hereafter the CPMG-NMR data by taking the Se-cluster distribution in the ideal/random case (refer to =0 in Fig. S1b) as the only reliable reference. While the Se-cluster fraction of the 0-Cd type species nearly matches the nominal ( =0) value (within a few percent), the Se-cluster species of 1-Cd and 2-Cd types are substantially over-and sub-represented with respect to the reference values, respectively. This suggests a clustering mechanism specifically concerned with the minor Se-cluster species of the 2-Cd type, in which part of the latter clusters "decompose" into Seclusters of 3/4-Cd types by driving off Zn atoms which eventually substitute for Cd within part of the remaining Se-clusters of the like 2-Cd type, thereby "recomposed" into Se-clusters of 1-Cd type. Altogether, the net effect is to favor Se-clusters of 1-Cd type to the detriment of Se-clusters of the 2-Cd type -as emphasized by antagonist arrows in Fig. S1b, while leaving unaffected the fraction of Seclusters of the ultimate 0-Cd type.
The above clustering mechanism selectively impacting the minor (detectable) Se-cluster species suffices to explain all disconcerting aspects of the Se-cluster distribution revealed by the current Zn0.83Cd0.17Se CPMG NMR spectra. It is further globally consistent with the existing insight into the nature of the Cd⇿Zn substitution in Zn1-xCdxSe earlier gained via the Raman spectra treated within the percolation scheme using the -formalism 19 .
By focusing on the minor Se-cluster species of 2-Cd type as the key of the clustering mechanism, a tentative (though not strictly relevant -as discussed above) value of ~0.12 can be inferred for Zn0.83Cd0.17Se from the CPMG NMR spectrum (Fig. S1b). This is significantly less than the Raman estimate of ~0.5 mostly derived at moderate/large Cd content 19 , reflecting a massive clustering. Such discrepancy occurs because the Raman and NMR techniques operate at different length scales, as briefly discussed below.
As the percolation scheme relies on a phenomenological (1D) description of a zincblende-type mixed crystal at the mesoscopic scale in terms of a composite of its two parent-like sub-regions, the Raman-based -insight is likewise relevant at the mesoscopic scale only. In this case is determined from the intensity ratio between the two like Raman modes due to the same bond species stemming from the two regions of the composite: one experimental/observable data (the above-mentioned Raman intensity ratio) vs. one adjustable parameter ( ) leads to an exact solution, meaning that the -formalism 8 is naturally applicable to the Raman spectra of a mixed crystal discussed within the percolation scheme. In contrast, by addressing separately the five possible first-neighbor (3D) cluster units (centered on the invariant species, with substituents at the vertices) forming a (real) zincblendetype mixed crystal, the NMR measurements provide an insight into the nature of the atom substitution at the ultimate microscopic scale. In this case it is rather unlikely that a single physical parameter ( ) suffices to govern the relative fractions of five different cluster units measured by NMR at a given composition, meaning that , in general, the -formalism 8 will fall short of explaining the NMR spectrum of a mixed crystal. In fact, NMR is likely to reveal how intricate a given deviation with respect to the ideal random substitution in a mixed crystal can be at the very local scale, beyond the -formalism.
2. Zn0.83Cd0.17Se: statistical insight into the Cd-Se bond percolation The parameter of local clustering mentioned above was originally introduced in Ref. 8 for a A1-xBxC zincblende-type lattice via the probability for the neighboring site besides a site occupied by X standing for A or B to be also occupied by X, leading to = + • (1 − ), with a similar definition. = 0 refers to the random A⇿B substitution, whereas a trend to clustering is reflected by > 0, limited by = 1 corresponding to full clustering, i.e., the local phase separation. With local clustering the bond percolation threshold is presumably not the same as in the random case. As an ultimate case of clustering, consider that all B substituents dispose onto the (A,B) sublattice so as to form a continuous chain perpendicular to the [111] direction along which the (A,B)-substituent and C-invariant planes alternate. In this case, a very small fraction of B substituents suffices to create the wall-to-wall B-C bond percolation : For a 3 -cubic supercell with (111)-oriented basal planes, the exact amount corresponding to B-C percolation from bottom to top scales as 1 2 ⁄ (= 3 ⁄ ), tending to zero when approaches infinity.
Based on the NMR and Raman measurements (Sec. IA), the studied Zn0.83Cd0.17Se crystal exhibits a trend towards clustering. One may well wonder whether the clustering may either hasten or delay the Cd-Se bond percolation with respect to the random case. Such information is required to get a rough idea of the mesostructure of the used Zn0.83Cd0.17Se crystal.
Technically we proceed as follows, using MATLAB as a programming language. In the zincblende Zn1-xCdxSe lattice the (111)-oriented dense-packing Zn1-xCdx-substituent planes alternate with corresponding invariant Se-type planes with similar packing, so that each invariant (Se) is tetrahedrally bonded with four substituents (Cd,Zn), and vice versa. Accordingly, to estimate the Cd-Se bond percolation on the Zn1-xCdxSe zincblende lattice in its ( , )-dependence we suppress the invariant Sesublattice and estimate the Cd-site percolation threshold on the remaining face-centered cubic (fcc) Zn1-xCdx-lattice. In fact, extensive Monte Carlo simulations S6 done on a virtually infinite (containing 2048 3 sites) fcc A1-xBx lattice provide a refined estimate of the site percolation threshold across the high-density (111)-packing planes in case of a random A⇿B substitution, i.e., ~0.19.
Our ambition is not to provide an exact estimate of the bond percolation threshold for a set value, but rather to compare the bond percolation thresholds at different values. Accordingly, finitesize fcc Zn1-xCdx-supercells containing a moderate (10 3 ) number of sites, that save computer time, are sufficient for our use. The (111)-fcc stacking is of the … -1 -2 -3 -1 -2 -3 -… type (Fig. S2), so that each site of plane number N hangs up on top of the middle of a trio of sites from the underlying N-1 plane, forming altogether a tetrahedral arrangement. The complete zincblende-type Zn1-xCdxSe lattice is restored by (virtually) inserting one Se atom in the middle of each (Cd,Zn)-tetrahedron. In practice we build up a series of 10 3 -sites fcc Zn1-xCdx-supercells with a (111)-oriented basal plane, and examine the wall-to-wall site percolation along the [111] direction from bottom to top of the supercell.
A reference curve obtained by plotting the probability ( ,~0) for site percolation on the random fcc Zn1-xCdx-lattice for spanning the entire composition domain with a constant step increase Δ =0.01, is shown in Fig. S2 (hollow symbols). Each point results from a statistical average over one hundred supercells. The supercells are generated so as to roughly match the set =0 value at each composition. This is achieved through enumeration of the five possible Se-centered tetrahedral units (with Zn and/or Cd at the vertices) and subsequent comparison with the predicted fractions using the binomial Bernoulli distribution at =0 8 . In case of significant disagreement (the accuracy is given below), a basic simulated annealing procedure is applied, consisting of successive Zn⇿Cd exchanges generated at random throughout the supercell (in practice one Cd atom taken at random is replaced by a Zn atom, and, at the same time, one Zn atom, also taken at random, is replaced by a Cd atom, thus preserving the same stoichiometry), until the fractions of clusters reasonably match (within ±5%) the nominal Bernouilli's estimates at the set =0 value. In the Se-cluster-enumeration process special attention is awarded to the minor cluster species at the studied composition -whose fraction is dramatically -dependent, but all cluster fractions are eventually checked to be consistent with the Bernouilli's prediction.
The above substitution procedure is adapted to design a reference series of supercells representing the partially clustered ( >0) Zn0.83Cd0.17Se mixed crystal. The targeted clustering rate is ~0.5, corresponding to the upper estimate for this crystal given the Raman and RMN insights (Sec. I1) -the desired value further appears to be the highest achievable value for the used supercell size. In the first place, the attention is focused on the minor Se-centered cluster (with four Cd atoms at the vertices, at this composition) constituting a sensitive marker of clustering. In fact, at x=0.17 by increasing from 0 to 0.5 the nominal Bernoulli's fractions 8 of Se-clusters dramatically change from (~47.5 %, ~39.0 %, ~12.0 %, ~1.7 %, ~0.3 %) to (~64.7 %, ~21.5 %, ~3.0 %, ~3.0 %, ~8.0 %), with percentages ranked in order of increasing Cd atoms at the vertices of the Se-clusters. Starting from a primary supercell generated at random, hence generally corresponding to a quasi negligible fraction of the minor Se-cluster species, the value is artificially increased by leaving the few existing minor clusters unchanged and realizing a random Zn⇿Cd exchange (as described above) specifically concerned with the alternative Se-cluster species. Such exchange is retained provided it generates a net increase of the value. The procedure is repeated until the targeted value is eventually achieved. The as-obtained "final" supercell (at ~0.5) is eventually retained only if the fractions of the four remaining Se-cluster species are further consistent (within ±5%) with the Bernouilli's estimates at the set ~0.5 value (as specified above).
We have checked that the same -trend persists with the wurtzite structure (full symbols in Fig.  S2) that exhibits nearly the same bond percolation threshold as the zincblende structure S6 , even though the (111) planes now alternate in a … -1 -2 -1 -2 -… sequence. The -trend in question is thus not structure-dependent for a given (A,B) vs. C tetrahedral environment.
B. Zn1-xCdxSe: a high-pressure X-ray diffraction study High-pressure X-ray diffraction measurements are performed on Zn1-xCdxSe with various compositions, crystallizing in the zincblende (x<0.3), mixed zincblende/wurtzite (0.3≤x≤0.7) and wurtzite (x>0.7) structures 19 at ambient pressure at the PSICHE beamline of the SOLEIL synchrotron using the 0.3738 Å radiation, with a double aim. The first one is to determine the critical pressure corresponding to the zincblende/wurtzite ⇿ rock-salt structural transition as a function of x, and the second one is to derive the x-dependence of the bulk modulus at ambient pressure for Zn1-xCdxSe taken dominantly in its zincblende structure -abbreviated 0 ( ) hereafter.
At each composition, a piece of Zn1-xCdxSe monocrystal is ground into a fine powder and inserted inside a 200 µm thick stainless-steel gasket preindented to 35 and drilled by spark-erosion to ~150 placed into the same Chervin type diamond anvil cell 40 (DAC) as that used for the high-pressure Raman measurements, with 300 m in diameter diamond culet. Neon was preferred to methanolethanol-water as a pressure transmitting medium 41 because the high-pressure X-ray diffraction measurements were pushed up to pressures exceeding by far the critical pressure corresponding to the hydrostatic limit of the latter medium, i.e., ~10 GPa. The measurements were performed both in the upstroke and downstroke regimes. The pressure was measured via the reference X-ray diffraction lines originating both from Au markers S7 added besides the samples inside the cavity of the DAC or/and from the neon transmitting medium itself S8 (depending on the pressure domain). An external setup was used to monitor the pressure inside the DAC from the computer room, i.e., without entering the experimental hutch. This helped to achieve a maximum accuracy in the pressure estimate (±0.3 GPa), while saving considerable recording time. The 0.3738 Å synchrotron radiation was focused onto a 40 diameter spot at the sample position, and the diffraction pattern was recorded using a plane detector disposed at about 30 cm of the sample (measured with LaB6 diffraction). The resulting 2D image plate data were then turned into intensity versus 2 plots using the software FIT2D S9 . The peaks fitting and unit cell fitting was carried out using the software DIOPTAS S10 .
A representative series of Zn0.83Cd0.17Se diffractograms is displayed in Fig. S3 where the diffraction lines are indexed by using the Miller indices. In the upstroke regime the first occurrence of the rocksalt phase is detected at Pmin.=11.3 GPa, i.e., slightly below the corresponding critical pressure for pure ZnSe (~13 GPa), as expected (see main text). The full disappearance of the native zincblende phase occurs at Pmax.=13.6 GPa, corresponding to a zincblende-rock-salt coexistence domain as large as ~2.3 GPa at ambient temperature. In the downstroke regime the crystal transits to the zincblende structure, starting at ~9.5 GPa via the transient cinnabar, a common feature at small-moderate Cd content -including pure ZnSe 7,S11 .
The pressure dependence of the unique (a: cubic symmetry) or double (a, c: hexagonal symmetry) lattice constants (specified in brackets) for all studied Zn1-xCdxSe mixed crystals on the way forth to the cubic/rock-salt phase, and, from there, on the way back to the native cubic/zincblende or hexagonal/wurtzite phases at ambient pressure, via in certain case the hexagonal/cinnabar phase, is recapitulated in Fig. S4. This offers a direct insight into the existence domains of each phase in both the upstroke and downstroke regimes, and helps to determine the composition dependence of the critical pressure transition to rock-salt, denoted , reported in Fig. S5 and in Fig. 1 as the average between the pressures corresponding to the onset of the rock-salt phase and the subsequent disappearance of the zincblende/wurtzite phase of all studied systems in the upstroke regime. An error bar is accordingly assigned to each value. The basic trend is that decreases when the Cd content increases, as expected -referring to (v) / main text.
The data displayed in Fig. S4 are further exploited to derive the 0 ( ) dependence for the studied mixed crystals throughout the zincblende domain, including Zn0.63Cd0.37Se -on account that this mixed crystal is dominantly of the zincblende type (only traces of the wurtzite structure are visible in its X-ray diffractogram taken at a near-ambient pressure -see Fig. 1 of Ref. 19) -besides Zn0.925Cd0.075Se and Zn0.83Cd0.17Se that both exhibit a pure-zincblende structure. 0 ( ) was inferred by fitting the variation of the unit-cell volume ( 3 ) to a Murnaghan equation of state maintaining for the pressure derivative of the bulk modulus ′ =4 S12 . The corresponding 0 ( = 0) value of the pure ZnSe compound with zincblende structure S13 is added for reference purpose.
The symbols in Fig. S5 refer to the 0 ( ) values resulting from averaging over various estimates obtained at all studied pressures at a given composition. The upper and lower limits of the error bars assigned to the average 0 ( ) values refer to the maximum and minimum estimates throughout all studied pressures at the considered composition, respectively. If we omit the error bars and focus on the average 0 values, it seems that 0 goes through a maximum around the Cd-Se bond percolation threshold, in echo to the predicted singularity in the ( ) dependence by ab initio calculations 11 . Such anomaly cannot be accounted for by the smooth VCA-like Vegard's law predicted based on ab initio calculations done with periodically-repeated ordered (8-atom) Zn1-xCdxSe supercells (x=0.25, 0.50, 0.75 together with the end compounds) S14 . Additional measurements are needed to decide whether the currently observed experimental singularity in 0 ( ) is intrinsic to the statistics behind the substitutional disorder in Zn1-xCdxSe, i.e., the result of the Cd-Se bond percolation throughout the ZnSelike host matrix, or merely fortuitous, i.e., reflecting a weak experimental insight that may not deserve attention given the too small number of studied compositions so far.
At this stage, we mention that reaching a maximum in a mechanical property of Zn1-xCdxSe by crossing the Cd-Se bond percolation threshold is not so intuitive. Indeed the Cd-Se bond is more ionic than the Zn-Se one (by ~12%, see Ref. 24) and thus less mechanically resistant to the inherent stresses in shear and compression/tension resulting from the contrast in bond length/stiffness of the two species. This gets reflected both at the macroscopic scale through a smaller value of the bulk modulus for CdSe than for ZnSe (by ~19% if we refer to the comparative ab initio insight of both cited systems taken in the zincblende structure given in Ref. S14), and also, at the microscopic scale, based on our estimate of the effective bond-stretching force constant (by ~7%) as the reduced mass of the bond multiplied by the square TO Raman frequency (using the values given in Ref. 19). On the above basis, one would rather expect a softening of the Zn1-xCdxSe lattice on crossing the Cd-Se bond percolation threshold, and not a hardening.
C. Zn0.83Cd0.17Se: a high-pressure Raman scattering study By inserting a tiny piece of a zincblende-type single crystal with parallel (110)-oriented crystal faces (obtained by cleavage) inside a diamond anvil cell and combining the backward and near-forward scattering geometries, one is in a position to address the pressure dependence of the long-wavelength (q~0) optic modes in their full variety, as detailed below.
The classical backscattering (reflection-like) setup, corresponding to the maximum value of the wavevector transferred to the crystal, of the order of ~1% of the Brillouin zone size, probes the transverse optic modes in their asymptotic purely-mechanical regime (abbreviated TO) away from the center Γ (q=0) of the Brillouin zone. By adopting the alternative near-forward scattering (transmissionlike) geometry, the wavevector transferred to the crystal is reduced by about two orders of magnitude and reaches minimum, offering an access to the same transverse optic modes but now taken in their asymptotic phonon-polariton (PP) regime close to Γ. Obviously, the near-forward scattering geometry can be implemented only if the used crystal is transparent to the incoming laser beam. In practice, for PP detection the scattering angle between the wavevectors of the incident laser beam and of the detected scattered light inside the crystal must not exceed a few degrees. Otherwise, one falls short of penetrating the actual phonon-polariton regime and remains stuck inside the asymptotic backscattering-like regime of the purely-mechanical TO modes 10,32,33 .
Though the LO modes are theoretically forbidden at (nearly) normal incidence/detection onto the (110) crystal faces of a zincblende crystal 31 , they show up clearly in both the backward and forward scattering geometries, due to multi-reflection of the laser beam between parallel crystal faces 32 . The multi-reflection is likewise responsible for the co-emergence of the TO and PP features in a highpressure Raman spectrum. Basically, on its way forth to the top crystal face (detector side) the laser beam generates the PP (forward-like) Raman signal, which superimposes onto the TO (backscatteringlike) Raman signal produced by the laser beam on its way back to the rear crystal face after reflection off the top surface.
Summarizing, provided the scattering angle reaches minimum with a relevant laser line, the TO, LO and PP modes may well come together in a high-pressure Raman spectrum, offering an overview of all Γ-like optic modes in a single shot. A representative series of such "complete" near-forward Raman spectra taken at various pressures with a (110)-oriented Zn0.83Cd0.17Se single crystal by using a green laser excitation (514.5 nm) -from which are selected those shown in Fig. 2 -is displayed in Fig.  S6a. A corresponding series of PP-deprived high-pressure Raman spectra taken in the backscattering geometry by using another green laser line (532.0 nm) and with the same crystal now ground as a powder is shown in Fig. S6b, for reference purpose. Note that in the latter powder-based experiment both the TO and LO modes are allowed owing to the lack of crystal orientation.
1. Contour modeling of the high-pressure backward/near-forward Zn0.83Cd0.17Se Raman spectra Contour modeling of the three-mode {Cd-Se, (Zn-Se) Zn , (Zn-Se) Cd } Zn0.83Cd0.17Se high-pressure Raman lineshapes in the main text, covering the purely-mechanical (TO) ones and their polar variants in the transverse (PP) and longitudinal (LO) symmetries, was achieved by using our generic expression of the multi-mode Raman cross section given in Ref. 19 and established in Ref. S15. Only, the resonance term, i.e., is the transferred frequency in a Raman experiment (defined in the far-infrared/phonon spectral range), differs in each case, depending on the magnitude of the transferred wavevector ⃗ in a Raman experiment, with → ∞ for the TO modes, finite for the PP modes and = 0 for the LO ones (see detail for a pure compound, e.g., in Ref. 14). In principle the pressure dependence of the resonance term can occur on the one hand, through ( , ) that captures the whole phonon behavior of Zn1-xCdxSe and through that refers to the used scattering geometry. For a given external scattering geometry the value is further dependent on the dispersion of the refractive index ( ) around the used laser excitation. In fact the pressure dependence of ( ) matters only for the PP modes characterized by finite values, whereas the pressure dependence of ( , ) is crucial for all modes.
Additional input parameters involved in the pre-factor of the resonance term of the Raman cross section are the Faust-Henry coefficients − of the Cd-Se and Zn-Se bonds, that represent the relative Raman efficiencies of the non-polar TO modes to the polar PP and LO ones. Such coefficients scale as the fractions of corresponding oscillators S16 in the considered three-mode {Cd-Se, (Zn-Se) Zn , (Zn-Se) Cd } system, i.e., as { , (1 − ) 3 + 2 (1 − ) 2 , 2 (1 − )}, correspondingly, reflecting a sensitivity of the Zn-Se vibration to its local 1D-environment at the second-neighbor scale 19 . The parent − values at ambient pressure are given in Ref. 19. As the − coefficients do not count for the resonance term itself, and thus play a minor role in our calculations, we consider that they are not pressure dependent in the following, in a crude approximation.
1-a. Pressure dependence of ( , ) in the resonance term of the Raman cross section The main ingredient in the resonance term of the Raman cross section is the relative dielectric function ( , ) of Zn1-xCdxSe. As the latter system appears to be of the "opening" type under pressure (see main text), meaning that no pressure-induced crossing occurs between any of its three TO oscillators, these can be considered as independent (uncoupled) in a first approximation. In this case, ( , ) takes the classical form (1) which includes an electronic background ∞ ( ) that scales linearly with between the parent ∞, values -representing the asymptotic limit of ( , ) at frequencies well-beyond the phonon resonances -together with three Lorentzian functions standing for the various TO oscillators. In Eq.
(1), , , , ( ) and 0, are the fraction of oscillator in Zn1-xCdxSe (given above), the phonon damping (coming via a friction force in the force assessment per bond) -corresponding in practice to the full width at half maximum of the -like TO Raman peak, the frequency of the observed TO mode due to oscillator in the Raman spectra of the mixed crystal, and the oscillator strength awarded to the related pure compound, namely CdSe ( =1) or ZnSe ( =2,3), respectively. In fact, 0, is expressed where Ω 2 = , 2 − , 2 refers to the TO-LO splitting of the -type compound 8 . In all reported simulations is taken minimal (1 cm -1 ), for a clear resolution of neighboring features.
Regarding the pressure dependence of ∞ ( ), we assume that the slight bowing ( =-1.55) evidenced at ambient pressure using ab initio calculations persists at any pressure S17 . Only, our reference ∞ value for ZnSe is rescaled to that measured at ambient pressure using spectroscopic ellipsometry S18 . The latter value does not exhibit any significant pressure dependence throughout the studied pressure domain (0 -10 GPa) in the ab initio calculations reported in Ref. S19 (no dependence) and in Ref. 42 (the variation is less than 2%). We assume the same for CdSe taken in the zincblende structure -for which the corresponding data are lacking in the literature.
The pressure dependence of the phonon oscillator strengths 0, awarded to the zincblende ZnSe compound is well documented. The TO and LO Raman frequencies of pure ZnSe were studied in detail by between ambient pressure and 10 GPa, and found to adopt the generic form ( ) = 0 + − 2 , with ( , )=(5.50, 0.0497) and (4.79, 0.137), respectively 47 . The resulting ∞ (see above) and ( ) trends for ZnSe generate a quasi linear collapse of the ZnSe oscillator strength versus pressure, with a final oscillator strength at 10 GPa scaled down the reference value at ambient pressure by ~36%.
Equivalent ( ) data are not available for CdSe because this compound does not crystallize in bulk in the zincblende structure at ambient pressure. Only thin films can be grown, which are not so convenient for optical measurements under pressure. Now, a linear pressure dependence of the LO Raman frequency was measured up to 5 GPa using CdSe clusters (35-55 Å in diameter) with zincblende structure S20 testified by X-ray diffraction. At ambient pressure the X-ray diffractograms of such clusters indicate a lattice constant (6.05±0.6 Å) matching the bulk value (6.052 Å) S21 . Therefore, along with the cited authors, we consider that the linear dependence is presumably valid for the bulk zincblende CdSe crystal. By assuming further that the linearity is preserved up to 10 GPa, the predicted upward shift of the LO frequency between ambient pressure and 10 GPa reaches 43 cm -1 . A similar variation for the TO frequency is still lacking in the literature. However, ab initio calculations reveal that the TO-LO splitting of CdSe near Γ is virtually identical in the zincblende and wurtzite structures S22 . Only, in the wurtzite case the TO-LO splitting is somewhat blurred by the increased diversity of optical phonon branches. This is due to the lowering of the crystal symmetry when shifting from the zincblende (cubic -isotropic) structure to the wurtzite (hexagonal -uniaxial) one, which duplicates the TO and LO modes into their so-called 1 and 1 variants -corresponding to ion vibrations along and perpendicular to the singular crystal axis, respectively. Despite the blurring, one may well think of resorting to the wurtzite structure for a crude insight into the pressure dependence of the TO-LO splitting. However, such approach is not applicable since the wurtzite CdSe crystal is not documented with this respect in the literature. At this point we can hardly proceed, except by analogy with another crystal. CdS is a natural candidate owing to its proximity to CdSe, regarding not only the lattice dynamical properties (the phonon dispersions of CdSe and CdS resemble very much, in both the zincblende and wurtzite structures) but also the elastic and electronic ones S23-S25 . Moreover CdSe and CdS take the same remarkable path via the transient zincblende structure (cubic, coordination number 4) to transite from wurtzite (hexagonal, coordination number 4) to rock-salt (cubic, coordination number 6) under pressure S26 . Further, the pressure domain over which the latter two-step structural transition develops is roughly the same for both systems S27 (1.5-3 GPa). To recollect with the raised issue, recent calculations performed with the wurtzite-type CdS crystal using a shell model-based interatomic potential indicate a quasi linear reduction of the TO-LO splitting by increasing pressure up to 5 GPa S28 , i.e., by ~37.5%. We assume that the TO-LO bands of the wurtzite-and zincblende-type CdSe crystals shrink at the same rate versus pressure up to 10 GPa, in a crude approximation. In this case the TO-LO splitting of the zincblende-type CdSe crystal, estimated to ~20 cm -1 at ambient pressure S22,S23 , falls to ~8 cm -1 at 10 GPa. With this, the remaining amount of oscillator strength for the zincblende-type CdSe crystal at 10 GPa hardly represents ~30% of the reference value at ambient pressure. We further assume a linear dependence on pressure.
1-b. Pressure dependence of ( ) in the resonance term of the Raman cross section The dispersion ( ) of the refractive index of Zn0.83Cd0.17Se measured at ambient pressure throughout the visible spectral range by applying spectroscopic ellipsometry to a large single crystal taken from the bulk ingot is shown in Fig. S7 (symbols; a truncated version of the current data setsufficient for our use -has earlier been reported in Ref. 19). A maximum is observed close to the optical band gap, estimated at ~2.488 eV at ambient pressure from a direct (model-free) numerical inversion of the measured raw ellipsometry angles. The full data set is adjusted via a polynomial fit for future analytical use (plain line).
The reported ( ) dispersion is a major ingredient into the multi-PP Raman cross section of Zn0.83Cd0.17Se, coming via the expression of the dimensionless parameter = 1 ⁄ that conveniently substitutes for the magnitude of the wavevector transferred to the crystal in a Raman experiment. In this expression 1 arbitrarily refers to the TO Raman frequency of pure ZnSe (~207 cm -1 ) 19 and is the speed of light in vacuum. The conservation of impulsion that governs the Raman scattering, i.e., ⃗ = ⃗⃗ − ⃗⃗ , where ⃗⃗ and ⃗⃗ refer to the wavevectors of the incident and scattered lights forming the scattering angle inside the crystal, leads to = ( 2 − 2 − 2 ) 1 2 ⁄ with , = −1 ( , ) , and , referring to the frequencies of the incident (laser) and scattered lights -with obvious subscripts. The resulting ( − ) = ( ) dispersion achieved experimentally with the used laser line ( ) for a certain scattering angle provides the so-called ( , )-Raman scan line (used in the main text). By injecting the experimental ( ) dispersion inside the resonance term of the Raman cross section, one obtains the Zn1-xCdxSe multi-PP Raman cross section in its ( , ≡ , ) dependence at ambient pressure.
For a given visible laser excitation the minimal value is achieved in the perfect forward scattering geometry ( = 0°), corresponding to = | ( ) • − ( ) • |. As the ( ) dispersion of Zn0.83Cd0.17Se is positive ( increases with ) throughout the visible (where operates the Raman scattering), | ( ) − ( )| works along | − | in the above expression, so that = 0 can never be achieved experimentally. As the ( )⁄ derivative increases with below the optical band gap of Zn1-xCdxSe, a smaller value is achieved by adopting the Stokes scattering geometry ( > , our approach) than the anti-Stokes one ( < ). Indeed, in this case the | ( ) − ( )| difference is minimal for a given | − | frequency gap (whichever laser excitation -in reference to , is used), with concomitant impact on the value, being also minimal. We have discussed elsewhere in extensive detail 19 that out of our available near-infrared (785.0 nm), red (632.8 nm), green (514.5 nm) and blue (488.0 nm) laser excitations, optimal conditions to probe the sensitive bottleneck region of the PP dispersion of Zn0.925Cd0.075Se (~2.615 eV) are achieved by using the green excitation at nearly normal incidence/detection onto/from (110)-oriented crystal faces. This remains basically valid for the current Zn0.83Cd0.17Se system, with a close composition.
In Fig. 2 the relevant value behind the experimentally detected PP Raman modes at a given pressure is estimated theoretically, i.e., by adjusting the Raman scan line (via ) until it intercepts the PP dispersion of the crystal right at the observed PP frequencies. Care must be taken that both the PP dispersion and the Raman scan line are pressure dependent, i.e., via both the TO frequencies and the refractive index of the crystal. In our approach a rough estimate, sufficient for our use, is obtained by neglecting any distortion of the light path due to the diamonds framing the studied Zn0.83Cd0.17Se crystal in the DAC. Only the refractive index of Zn0.83Cd0.17Se is taken into account. In fact, the difference in refractive index is small between diamond and Zn0.83Cd0.17Se (less than 8% at 700 nm at ambient pressure), and the change in refractive index versus pressure for diamond is negligible compared to that of Zn0.83Cd0.17Se (by a factor of ~15) S29 , meaning that most of the pressure dependence of the refractive index of the studied diamond/ Zn0.83Cd0.17Se /diamond system in the DAC is due to Zn0.83Cd0.17Se. The approximation is further justified in that the provided values in this work are indicative only; these are not discussed as significant physical parameters per se.
An experimental measurement of the pressure dependence of the ( ) dispersion of Zn0.83Cd0.17Se is a difficult task. Indeed, effective spectroscopic ellipsometry measurements usually require a large sample area, typically of the order of several mm 2 , and therefore cannot be made in a DAC. The difficulty can be circumvented by resorting to theory. Ab initio calculations done on pure ZnSe 40 reveal that its optical band gap widens under pressure, dragging with it the ( ) dispersion in an overall translation towards low wavelength (high frequency/energy) at a rate of ~5 nm/GPa. We assume the same for the currently studied Zn0.83Cd0.17Se crystal with a large ZnSe content, with the optical band gap of this mixed crystal at ambient pressure taken as a set point. The ( ) dispersions of Zn0.83Cd0.17Se at 5 GPa (dotted line) and 9 GPa (dashed line) resulting from such overall translations are displayed in Fig. S7 besides the experimentally measured ( ) curve at ambient pressure (symbols), used as the reference/starting curve.
2. Zn0.83Cd0.17Se: experimental results and discussion By applying pressure, the PP dispersion is right-shifted in Fig. 2 (i.e., horizontally) due to a highfrequency shift of the asymptotic TO (away from Γ) and LO (close to Γ) modes resulting from a strengthening of the related effective bond force constants. In contrast the Raman scan line is upwardshifted towards Γ (i.e., vertically) due to the reduction of the ( ) dispersion around the used laser excitation (Fig. S7). The Raman scan lines obtained in the perfect forward scattering geometry ( = 0°) depending on pressure are shown in Fig. 2, for reference purpose. For any detected PP signal the experimentally achieved values lie in the range 0.5 -0.8°. This falls close to the minimal achievable value ̅~0 .15° taking into account an experimental limitation that the scattered light is not strictly detected perpendicularly to the sample surface but fits into a pencil cone due to the finite numerical aperture of the used microscope objective for the detection (see Methods).
At ambient pressure (0 GPa) no PP is detected. Most probably, the reason is that as soon as a PP mode emerges, it interferes destructively via a Fano-type coupling with the spurious two-phonon continua of transverse acoustic modes -abbreviated 2TA -that shows up nearby. In fact, the native TOs behind the searched PPs are already corrupted by such Fano interference, testified by their farfrom-perfect TO Raman selection rules (see Fig. 7b of Ref. 19). The TO-distortion via the Fano-coupling involving the 2TA continuum is a general feature of ZnSe-based systems. In the case of Zn0.83Cd0.17Se the coupling is merely seen through a slight subsidence of the baseline on the low-frequency tail of the TO mode, as observed in the pure TO symmetry at ambient pressure (marked by a star in Fig. 2). In some cases the subsidence can develop into a pronounced antiresonance separating the TO mode from the incriminated 2×TA band, then showing up strongly in the Raman spectra, as independently observed with Zn1-xBexSe 21 -an example is given below, and with Zn1-xCdxSe as well S30 .
Under pressure the zone-edge TA modes soften -the trend is aggravated for the 2TA band -in contrast with the zone-center optic (TO, LO) modes and the related (PP) features that harden 34 , as already mentioned. This leads to Fano-decoupling, offering a chance for PP detection (Fig. S6a). In fact, various PPs are detected at intermediate (~5 GPa) and high pressure (~9 GPa), if none at ambient pressure (~0 GPa).
At intermediate pressure (~5 GPa), the PP dispersion is probed on approach to the sensitive bottleneck region, corresponding to ~0.7°. The native − and − modes behind − and remain close so that the → − transfer of oscillator strength mediated by the macroscopic PP-like transverse electric field ⃗⃗ ( ) is massive. This results in the clear emergence of − , showing up strong and sharp, at the cost of , absent. At maximum pressure (~9 GPa), the Raman scan line now corresponding to ~0.5° probes the PP dispersion closer to the bottleneck where − , still distinct and sharp, starts to vanish away from its native − mode (off-shifted by ~20 cm -1 ). Remarkably now shows up as a weak but still pronounced shoulder significantly beneath its native − mode (by ~15 cm -1 ). This can be explained only if the native − mode behind − breaks away from − under pressure. In this case the ⃗⃗ ( )-coupling between − and is partially relaxed, with a consequence that retains sufficient oscillator strength to emerge as a distinct Raman feature. We have checked that, the detected − mode at ~5 GPa vanishes to full disappearance as soon as the scattering angle increases, as achieved by departing the laser beam from normal incidence at the rear crystal face (Fig. S6a). Also, at ~9 GPa, both − and slightly "retreat" towards their native TOs by changing the laser line from green (514.5 nm) to blue (488.0 nm), while keeping the same external incidence of the laser beam at the rear of the crystal (Fig. S6a). Altogether, such trends ascertain the PP nature of the discussed features. In fact, owing to their finite value (see above), the PP modes are strongly laser-and -sensitive, regarding both their Raman frequency and their Raman intensity (in contrast the TO and LO modes consist of "robust" features that emerge with similar characteristics whichever Raman scattering setup is implemented, at least out of resonance conditions).
Last, we address the LO modes with special attention to the minor intermediate one (Fig. 2). Our ambition is to infer the pressure-dependence of the native percolation-type ( − , − ) doublet behind the LOs from the experimentally observed strengthening/upward-shift-towards-+ of under pressure (Fig. 2). It is a matter to decide whether the spacing between the two ZnSelike TOs reduces (scenario1, closure case), is preserved as such (scenario 2, invariant case), or enlarges (scenario 3, opening case) when the pressure increases. A comparative study of is carried out between ambient pressure and 9 GPa using the LO-variant of the Raman cross section given in Ref. 19. The input parameters are the − and − frequencies taken from Fig. 2, and also the − one with some flexibility depending on the used scenario (1: spacing reduced by 10 cm -1 , 2: spacing maintained at 20 cm -1 , spacing enlarged by 10 cm -1 , with a proper rescaling of the ZnSe-like available oscillator between ambient pressure and 9 GPa as specified in Sec. ID1. As apparent in Fig.  S8, the combined strengthening/upward-shift of are simultaneously reproduced only under scenario 3, while neither of the trends comes out under scenarios 1 or 2. We conclude to the widening of the ( − , − ) percolation doublet under pressure. Last, we discuss briefly the PP-deprived high-pressure backscattering Raman spectra taken with powders (Fig. S6b), for the sake of completeness. A careful examination focusing on selected pressures corresponding to a reasonable resolution of the minor − feature supports via a direct insight into the underlying (broad, poorly-defined) TO modes behind the PPs the conclusion drawn from observation of the latter (sharp, well-resolved) modes (Figs. 2 and S6a) that − breaks away from − at increasing pressure (∆ enlarges, as emphasized by open-arrows). As for the upper − mode, a direct insight remains forbidden due to a screening by the (now allowed) signal, as by near-forward Raman scattering. Now, offers a convenient substitute for − due to their quasi degeneracy, as already mentioned 19 . As independently observed by near-forward Raman scattering (Fig. S6a) gets closer and closer to the dominant + feature at increasing pressure ( enlarges, as emphasized by plain-arrows -the trend is visible at least up to 8.1 GPa) and by doing so reinforces, as emphasized by the large upward arrow at 8.1 GPa. The LO nature of the pointed feature is verified as it collapses together with the upper + mode at maximum pressure, as emphasized by large downward arrows. In brief, the (TO,LO,PP) near-forward and (TO,LO) backward Raman spectra are consistent on the main trends for what regards the pressure-dependence of the underlying compact ( − , − , − ) triplet.
D. Zn1-xCdxSe: Ab initio lattice structure / dynamics calculations By construction, the ab initio calculations of the high-pressure Raman spectrum of a nominally random (~0) Zn0.5Cd0.5Se 216-atom zincblende supercell provided in the main text specifically refer to the optic modes of the corresponding mixed crystal near the center Γ (q~0) of the Brillouin zone. We emphasize that the used version of the AIMPRO code does not take into account the macroscopic electric field that is likely to accompany the long wavelength (q~0) lattice vibrations in such a polar crystal as a II-VI zincblende one (like Zn1-xCdxSe) -being clear that immediately away from Γ the problem disappears 16 . As such, the reported ab initio Raman insight relates only to the Γ-like TO modes taken in their non-polar (purely-mechanical) regime -of central interest for the reported discussion in the main text; it does not cover the corresponding polar LO modes also accessible by Raman scattering.
In the following we extend the ab initio (AIMPRO) study of the Zn1-xCdxSe lattice dynamics under pressure to the phonon density of states (PhDOS) calculated over the Brillouin zone using a series of disordered (~0) 216-atom Zn1-xCdxSe supercells with well-spanned Cd contents (x=0, ~0.3, ~0.5, ~0.7, 1) throughout the composition domain. Our aim is twofold. First, (i) such phonon overview throughout the Brillouin zone depending on pressure is important to judge directly whether or not the acoustic and optic bands of Zn1-xCdxSe separate under pressure, the sine qua non condition for detection of the PP's by near-forward Raman scattering (see main text). Also, (ii) it is interesting to examine whether the pressure-induced splitting of the three-mode {1×(Cd-Se), 2×(Zn-Se)} finite structure behind the Cd0.5Zn0.5Se ab initio Γ-like TO Raman signal -as evidenced in the main text (Fig. 2c) -further replicates in the PhDOS, i.e., throughout the Brillouin zone, and at various Cd contents, for the sake of completeness.
The Zn1-xCdxSe (x=0, ~0.3, 0.5, ~0.7, 1) PhDOS calculated with the AIMPRO code using 216-atom disordered (characterized by ~0 at x≠0,1 -see Methods) zincblende-type supercells (the used supercells at x~0.3 and ~0.7 only differ by switching Zn and Cd on the same sites) at ambient (0 GPa, thin curves) and high (10 GPa, thick curves) pressures are shown in Fig. S9. Generally, the current ZnSe and CdSe PhDOS are consistent on the main trends with available ones calculated via the ABINIT (ZnSe -Ref.  and SIESTA (CdSe -Ref. S23) ab initio codes, which gives confidence in the reported AIMPRO data, covering not only the parent systems but also the related mixed crystals.
The PhDOS of the parent and mixed crystals are characterized by three main bands. An intense optic band ( , becoming and for the parent compounds) at high frequency reflects the moderate dispersion of the optic branches. In contrast, the transverse (TA) and longitudinal acoustical (LA) branches are naturally dispersive, but tend to flatten near the edge of the Brillouin zone (zone-edge, abbreviated ZE). The ZE-flattening is especially pronounced for the TA branch, a common feature of zincblende-and diamond-type semiconductors due to the stabilization of such tetrahedral lattices by non-central bond forces 12,13 . Accordingly the ZE-TA PhDOS shows up more strongly than the ZE-LA one. The phonon dispersion curves of ZnSe and CdSe taken in the zincblende structure given, e.g., in Refs. S31 and S22-S23, respectively, constitute natural references with respect to such basic optic and acoustic trends. By increasing the Cd content, the optic and acoustic Zn1-xCdxSe PhDOS shift to low frequency, generalizing to the entire lattice dynamics (throughout the Brillouin zone) the Γ-like TO trend sketched out in Fig. 1b.
First, we address the PP-related issue (i). By increasing pressure the bonds shorten and at the same time become more covalent 12,13 . Both effects work along to strengthen the bond force constants, which "hardens" most phonon bands including the optic and ZE-LA PhDOS, with concomitant impact on the phonon frequencies, being upward shifted (as emphasized by arrows pointing to the right side in Fig. S9). One notable exception is the ZE-TA band that "softens" (shifts towards low frequency -see arrows pointing to the left side in Fig. S9). This reflects a collapse under pressure of the non-central bond forces stabilizing the lattice under shear (TA-like) distortion at short wavelength (ZE-like), the precursor sign of a pressure-induced structural transition 34 . The above generic optic and acoustic trends, evidenced experimentally with several Zn-based II-VI zincblende compounds 34 , are echoed in the current pressure-dependent Zn1-xCdxSe PhDOS.
At ambient pressure, the two-phonon ZE-(TA+LA) acoustical band, and also the ZE-2×TA one (to a less extent), are nearly resonant with the one-phonon Γ-like ( ) optic band (Fig. S9), which prevents the PP detection by Raman scattering, as already discussed (main text). As apparent in Fig. S9, the optic band ( ) hardens at a faster rate than the ZE-LA one under pressure both in ZnSe and BeSe, and the trend is preserved with the mixed crystals. Altogether the softening, moderatehardening and strong-hardening of the ZE-TA, ZE-LA and optic PhDOS, respectively, work along to enlarge the frequency gap between the one-phonon optic PhDOS and both spurious two-phonon ZEacoustic bands, thereby opening a channel for PP detection by near-forward Raman scattering at high pressure -as argued in the main text, in response to (i).
Now we turn to issue (ii) related to the pressure dependence of the fine structure behind the optic band ( ) of the mixed crystals. At ambient pressure the optic PhDOS of ZnSe, CdSe and the related mixed crystals cover comparable spectral ranges (~55 cm -1 ): in fact, the optic PhDOS of the mixed crystals are so compact that any fine structure is hardly visible, as in the Raman spectra (Fig. 2c, 0 GPa). Under pressure the ZnSe and CdSe optic PhDOS exhibit a significant broadening (~30% at 10 GPa), however not comparable to the dramatic spreading of the Zn1-xCdxSe optic ( ) PhDOS, roughly doubled with respect to ambient pressure. This reveals a distinct three-mode fine structure. The lower (~220 cm -1 ), central (~250 cm -1 ) and upper (~280 cm -1 ) features strengthen, collapse and are better resolved with increasing Cd content, respectively. This is consistent with their percolation-type assignment in terms of {1×(Cd-Se), 2×(Zn-Se)}-like bands, as in the Raman spectra (Fig. 1a). Summarizing, at all studied compositions the percolation-type fine structure behind the optic-PhDOS of the mixed crystals splits under pressure. This nicely recollects with the experimental (17 at. % Cd) and ab initio (~50 at. % Cd) Raman insights gained near Γ (main text). Note, tough, that the current optic-PhDOS combines the TO and LO insights whereas the cited Raman data are of the pure-TO type.
To conclude the ab initio (AIMPRO) study on Zn1-xCdxSe, and as a convenient introduction to the forecoming Raman study of Zn1-xBexSe in the next Sec., we find it useful to compare briefly the ab initio bond length distributions of both mixed crystals at intermediate composition (x~0.5) and at ambient pressure, in view to provide an insight into the lattice relaxation behind the lattice dynamics.
For the sake of consistency, we use the same 216-atom zincblende-type disordered (~0, x=0.5) supercell for both mixed crystals -identical to that used to calculate the ab initio Zn0.5Cd0.5Se Raman spectra (Fig. 2c). In particular the Se and Zn positions are the same in both supercells, hence only differing by the type of cation, i.e., X=Cd or Be, on the remaining sites of the substituting (Zn1-xXx)sublattice already half-filled by Zn. The corresponding Zn0.5Cd0.5Se and Zn0.5Be0.5Se distributions of bond lengths after full relaxation (of the lattice constant and of the internal atom positions) are shown in Figs. S10a and S10b, respectively.
In order of increasing bond length, Be-Se comes first, then Zn-Se and Cd-Se last (the natural bond lengths in the corresponding pure zincblende crystals, i.e., 2.20 Å, 2.42 Å and 2.61 Å, respectively, are marked by vertical arrows, for clarity). Accordingly the (short) Zn-Se and (long) Cd-Se bonds suffer tensile and compressive strains in Zn0.5Cd0.5Se, respectively, and the same holds true for the (short) Be-Se and (long) Zn-Se bonds in Zn0.5Be0.5Se, correspondingly. Remarkably, in both cases the bond length distribution is broad/narrow for the short/long species. A similar trend was independently evidenced in Ga0.5In0.5P S32 , with similar difference in bond length 24 (∆ ⁄~7%) as Zn0.5Be0.5Se (∆ ⁄~10%) and Zn0.5Cd0.5Se (∆ ⁄~7%). This conforms to our view that the local strain due to the contrast in bond physical properties (length, stiffness) is mostly accommodated by the short species in a mixed crystal, irrespectively of the nature of the bond (Zn-Se is the short/stiff species in Zn0.5Cd0.5Se and the long/soft one in Zn0.5Be0.5Se, the stiff/short character referring to small/large bond ionicity 24 ). This supports our view that the percolation-type Raman doublet is better resolved for the short bond of a mixed crystal than for the long one (see main text -Introduction). Further, as expected on account that the BeSe-like Raman doublet of Zn1-xBexSe is better resolved than the Zn-Se Raman doublet of Zn1-xCdxSe -the frequency gap between the like sub-modes from the doublet is roughly double (Fig.  1a), the bond length distribution is broader for the (short) Be-Se bond of Zn0.5Be0.5Se than for the (short) Zn-Se one of Zn0.5Cd0.5Se. In a nutshell, a well-resolved percolation-type Raman doublet (lattice dynamics) apparently goes with a large diversification in bond length (lattice relaxation), as expected (see main text -Introduction).
We emphasize, though, that no straightforward one-to-one correspondence can be achieved between the Raman frequencies and the bond length distribution. This is because, in such a complex system as a mixed crystal, variations in the Raman frequencies are due to changes in the bond-bending and bond-stretching force constants resulting from complex bond distortions at the local scale in the real (3D) crystal related not only to the bond length but also to the bond angle S32 .

II. Zn1-xBexSe
A reference insight into the pressure-induced closing of the percolation-type Raman doublet in a mixed crystal can be achieved by focusing on the Be-Se doublet of Zn0.5Be0.5Se, as a case study. Generally, Zn1-xBexSe exhibits an unusually large contrast in its bond physical properties (length, reduced mass, stiffness), so that the percolation doublet due to its short/light/stiff Be-Se bond is, at the same time 21 , well resolved -with a splitting as large as ~45 cm -1 -and well-separated from the Raman signal due to the long/heavy/soft Zn-Se bond -vibrating at a lower frequency by as much as ~200 cm -1 . Moreover, at intermediate composition (~50 at. %Be) the fractions of the two Be-Se oscillators are identical in the crystal -given by 2 and • (1 − ) in order of ascending frequency (reflecting a sensitivity of the Be-Se vibrations up to first-neighbors in Zn1-xBexSe), with concomitant impact on the TO Raman intensities S33 . This is ideal to achieve a reliable insight into the pressure dependence of both individual submodes forming the Be-Se Raman doublet. Additional interest for a focus at ~50 at. %Be arises from the theoretical point of view, as detailed in the course of the presentation of the model at a later stage (see Sec. IIA).
Fig. S11a displays a representative series of high-pressure Raman spectra taken in the upstroke regime with a Zn0.48Be0.52Se powder from ambient pressure up to ~25 GPa, whichs remains below the critical pressure corresponding to the zincblende⇾ rock-salt structural transition, i.e., ~35 GPa S34 . A zoom into the BeSe-like TO and LO Raman frequencies in their pressure dependence is provided in Fig.  S11b (squares), for clarity. The assignment of various TO and LO modes in the Zn-Se and Be-Se spectral range is the same as in Ref. 21. Additional high-pressure Raman data currently taken both in the upstroke (hollow symbols) and downstroke (filled symbols) regimes with the same sample now prepared as a single crystal (circles) are added, for the sake of completeness. Both series of highpressure Raman measurements were performed by using methanol/ethanol/water (16:3:1) as a pressure transmitting medium. This remains hydrostatic up to ~10.5 GPa (Methods) and can be treated as quasihydrostatic until ~30 GPa.
The detailed study of the Zn-Se Raman signal initiated in Ref. 21, not central in the current study, was pursued in Ref. S35. In fact, part of the Zn0.48Be0.52Se Raman spectra shown in Fig. S11a were already published at this occasion (up to 7 GPa). The interest at the time was to clarify the rather confusing multi-mode Raman pattern in the Zn-Se spectral range, using pressure as a convenient tool, notably in search for possible ZnSe-like PP modes. In the current study the focus has shifted to the Be-Se Raman doublet of Zn0.48Be0.52Se, with the aim to understand its pressure dependence, in the same spirit as in our original contribution on Zn0.76Be0.24Se 21 . A noticeable improvement with respect to the latter pioneering contribution, that was centered on the TOs and qualitative only, is that the TOs and LOs are now treated on equal footing and on a quantitative basis.
Unambiguous experimental trends emerge from the reported data in Figs. S11a and S11b, listed as follows. Recollecting with the used notation in the main text, these enunciate as (i) the gradual convergence of the lower mode onto the upper one under pressure, (ii) accompanied by its progressive collapse until extinction at the crossing/resonance ( ), (iii) that occurs around the critical pressure ~15 GPa, (iv) corresponding to an apparent freezing of the lower oscillator independently testified by ab initio calculations done with Zn1-xBexSe 21 and ZnSe1-xSx 22 (using relevant impurity motifs in each case). Apparently, (iv) only the upper mode remains visible above ; the lower one has disappeared. However, it is not clear whether both modes survive as degenerated features above or whether only one has survived and the other has been 'killed' by pressure. Preliminary results obtained by examining the pressure dependence of the PP modes of ZnSe1-xSx tend to support the latter option 22 . Indeed, fair contour modeling of the PP Raman signal behind the Zn-S percolation-doublet depending on pressure could be achieved only by considering a progressive loss of the oscillator strength awarded to the lower mode until full extinction at the resonance. However, the PPs are not so reliable markers with respect to the addressed issue in that both the PP frequencies and intensities are so sensitive to the scattering angle and the used laser line, in contrast with the TOs and the LOs.
More generally, besides the persisting question of the "survival/death" of the lower mode post , neither the origin of its progressive collapse ante , nor the mechanism behind its crossing with the upper mode at , could be explained so far. The latter pending issues are addressed hereafter by focusing on the TO and LO modes constituting more robust markers than the PPs, using Zn0.5Be0.5Se as a model system.
A. The Be-Se doublet of Zn~0.5Be~0.5Se viewed as a damped system of coupled harmonic 1D-oscillators Generally, the above experimental/ab initio trends (i-iv) may look confusing at first. The progressive collapse of the lower TO mode when it gets closer to the upper mode under pressure reveals that the two (purely-mechanical) TOs are mechanically coupled. In this case one would expect a strong repulsion of both oscillators at the resonance corresponding to perfect tuning of the bare/uncoupled oscillators. In fact, the two modes do cross at , suggesting that the two TOs do not "see" each other and hence are uncoupled. The picture which emerges is that the presumed mechanical coupling between the two TOs is totally screened by an overdamping of the lower mode at the resonance (see main text). In this case the TOs are virtually decoupled by overdamping at the resonance, so that an actual crossing can occur. Altogether, this guides towards a coupled model of two damped 1D-harmonic (spring, mass) oscillators, as recently proposed 26 .
The cited authors developed an exhaustive analytical study of a viscoelastic system consisting of two damped purely-mechanical 1D-harmonic oscillators (with damping coefficients noted ; =1,2) corresponding to distinct masses coupled mechanically via a damped spring (with stiffness ′ and damping coefficient ′ ) -thereby introducing some anharmonicity -and to the lab. frame as well (with spring stiffness , =1 or 2, being not dependent on the mass displacement -in reference to the harmonic character of the bare oscillators).
Such description can be transposed almost literally to the treatment of the purely-mechanical TO modes forming the BeSe-like Raman doublet of Zn0.5Be0.5Se. In this case, the lab. frame refers to the surrounding Zn-Se bonds that constitute an obstacle to the Be-Se vibrations, simply because they naturally vibrate at a far-off frequency 21 . Only, in this case the two oscillators have identical mass ( ) -corresponding to the reduced mass of a Be-Se bond -because they both refer to the same bond species. Each Be-Se oscillator is attached to the lab frame via an effective spring-like bond force constant ( ) that varies depending on whether the Be-Se bond vibrates in the hetero (Zn-type: upper oscillator, numbered 1) or homo (Be-type: lower oscillator, numbered 2) environments -using the terminology of the percolation scheme. The vibration frequency of each bare, i.e., uncoupled, TO oscillator taken alone takes the classical form , = √ −1 , where assimilates with the effective Be-Se bond stretching force. For purposes of the model, a damping term ( ) is introduced by adding into each scalar (1D) equation of motion per oscillator a friction force (anti-proportional to the velocity ̇, with proportionality factor = ; =1,2) besides the spring-like restoring force to the lab frame − , where refers to the relative displacement of oscillator with respect to its position at rest representing in fact the effective Be-Se bond-stretching behind oscillator . In practice, monitors the full width at half maximum of the TO Raman peak related to the -like Be-Se oscillator. In contrast, the damping term ( ′ ) added to the coupling-spring ( ′ ) between the two (BeSe-like) oscillators has no physical meaning per se in that it does not relate directly to any oscillator. It is considered only as a convenient way to introduce the concept of exceptional point, which marks a separation between two regimes depending on whether the coupling (in reference to ′ ) dominates the damping (in reference to 1 and 2 ), or vice versa (a schematic view of the coupled/damped oscillator system is provided in Fig. 1) -see below.

Damping-dependent (TO,LO) coupled mode frequencies
The non-polar TO-like description worked out in Ref. 26 and outlined above can be generalized to their polar (electrical-mechanical) LO counterparts by adding to the force assessment per oscillator a Coulomb force created by the LO-like long range electric field ( ) due to the ionic character of the chemical bond in a zincblende crystal S36 . The Coulomb force involves the Born/dynamic charge of the Be-Se bond, noted , which monitors the magnitude of the TO-LO splitting related to the unique phonon of the BeSe end compound of Zn1-xBexSe 9 . In fact, the LO-like Coulombian interaction reinforces the purely-mechanical TO-like restoring bond force constant, so that the LO mode vibrates at a higher frequency (noted for the pure compound) than the TO one S36 (noted ). The asexpanded generic set of scalar (1D-like) equations of motion covering both the TO and LO modes of the considered two oscillator BeSe-like system takes the following form, (2b) where is taken independent of composition S16 , in a crude approximation. The justification for using a scalar version of the equations of motion per oscillator when discussing the long wavelength optical modes as detected by Raman scattering is given in the main text. We specify further that at such length scale the like Be-Se bonds of a given species all vibrate in phase throughout the crystal, so that a unique equation per oscillator (a Be-Se bond taken in a given environment, i.e., Be-or Zn-like) suffices to capture the whole dynamics of the like oscillators throughout the crystal 8 .
An additional equation is needed to govern the transverse (TO) or longitudinal (LO) character of the macroscopic electric field . This is derived from the Maxwell's equations via the relative dielectric function ( ) of the crystal, given by, 0 ( ) = 0 + 0 ∞ + ( 1 1 + 2 2 ).
(3) In this equation 0 is the permittivity of vacuum; = − is the transferred energy to the crystal in a Raman experiment; is the number of Be-Se bonds per volume crystal unit, and the fraction of oscillator (=1,2) in the crystal ( 1 + 2 = 1). The last term of Eq. (3) represents the (ionic, phononlike) contribution from both oscillators to the polarization of the crystal (considering each Be-Se bond as a permanent dipolar momentum). The intermediate term involves the susceptibility of a Be-Se bond at ≫ ,1 , ,2 , concerned with the electronic part of the crystal polarization.
The above system has non-trivial solution ( 1 , 2 ≠ 0) only if its determinant (abbreviated Det) vanishes. In its present form, due to the linear dependence on brought by the friction force appearing in the -terms, Det=0 consists of a general quartic equation. A more convenient biquadratic form likely to provide solutions coming in pairs -as ideally expected for a system of two coupled oscillators -was achieved 26 by removing the friction forces and substituting imaginary restoring forces (not in phase with the mass displacements, i.e., with the Be-Se bond stretching in our case) for the real ones in the force assessment per oscillator -referring to Eqs. (2). This lead to introduce the concept of anelastic damping, as formalized by operating a series of transformations on the -terms, schematically summarized as follows: , 2 + ′ 2 + (original expression) → , 2 + ′ 2 (by omitting the friction force) → , 2 (1 + ) + ′ 2 (1 + ) (each genuine spring constant is equipped with an imaginary part) → , 2 + , (the disruptive linear dependence on is suppressed).
At the end of the above -transformations, , 2 re-appears but with a different meaning as in its original -form. The final , 2 term is dictated not only by the intrinsic spring constant of the considered oscillator (i.e., ), as in the starting -expression, but also by the coupling spring constant between the two oscillators (i.e., ′ ). In our case it is important to preserve the starting , terms because these carry the frequency information on the bare TO oscillators ante coupling (see above). Therefore, we generally proceed as in Ref. 26 but take care to retain the original meaning for each individual term inside . This leads to consider * = , 2 + ′ 2 (1 + ) + , as the final form for , with concomitant impact on now expressed as * = * + Ω 2 2 ⁄ . is likewise re-written as * = (1 + ) − Ω 2 2 ⁄ . A star added as a superscript reflects the imaginary character of each term, for a clear distinction from its original (real) form.
Adopting * comes to consider a constant friction force at any frequency , in fact that suffered by the bare-uncoupled (TO) oscillator. Such approximation is valid as long as the coupling spring constant ( ′ ) remains small with respect to the intrinsic spring constants of both oscillators ( ), meaning that the frequencies of the coupled TO modes do not substantially differ from those of the bare-uncoupled ones. In fact, this is actually so with Zn0.5Be0.5Se, as discussed below. In this case keeps the meaning of a friction-like damping parameter corresponding to a physical observable in the Raman data, namely the full width at half height of a Raman peak, as already mentioned. As for the anelastic damping of the coupling spring constant apparent in the central term of * , its reason for being is that it becomes useful at a later stage in view to introduce the concept of "exceptional point".

The exceptional point: a pivot between the underdamped and overdamped regimes
The exceptional point of the TO-coupled system (Ω 2 = 0, specified via subscript ), corresponding to ( ,+ * ) = ( ,− * ), is achieved when the square-root-term in Eq. (8b) is at zero -meaning that both its real and imaginary parts are at zero -taking care to replace ′2 by ′2 (1 + ). The condition on the imaginary part leads to 1 ,1 − 2 ,2 = −4 ′2 ( ,1 2 − ,2 2 ) −1 . When injected in the equality to zero applying to the real part, the latter equality leads to a biquadratic equation on = ( ,1 2 − ,2 2 ) 2 whose only admissible solution obeys ,1 2 − ,2 2 = ±2 ′2 . The above two equations relate via (justifying a posteriori its introduction as an anelastic damping term related to ′ -see above), leading to 1 ,1 − 2 ,2 = ±2 2 near the resonance ( ), where = ′2 2 ⁄ . (9a) In fact, measures the strength of the mechanical-coupling between the two oscillators (via ′ ) compared to the intrinsic strength of each mechanical oscillator at the resonance (in reference to 1 and 2 , being equal at this limit). Strictly at the resonance, i.e., ,1 = ,2 = , the critical value = | 1 − 2 |⁄ (9b) is achieved. This gives a measure of the damping compared to the intrinsic strength of each mechanical oscillator at the resonance. Different regimes are achieved depending on whether > (coupling dominates over damping) or < (vice versa), separated by the so-called exceptional point characterized by = at the resonance 26 . From now on the interest for disappears, for our use at least. Hence is taken equal to zero in the next sections, with an immediate consequence that becomes real.
Incidentally, the exceptional point for the LO mode can be derived in the same way by adopting the relevant Ω 2 value (i.e., 2 − 2 ) and substituting ( ′2 − This leads to introduce a characteristic -like parameter for the LO modes, noted = | ′2 − Ω 2 2 | 2 ⁄ . The exceptional point for the LO modes, corresponding to an actual crossing of the LO frequencies, is then achieved for = . Note, that owing to the Ω 2 term, the exceptional point cannot be achieved simultaneously for the TO (Ω 2 = 0) and LO (Ω 2 ≠ 0) modes.

2-a. ≫
: the reference insight at zero damping ( 1 = 2 = 0; = 0) The absence of damping ( 1 = 2 = 0), corresponding to ≫ , is treated in the first place prior to examining the > and < cases in the subsequent Secs., for reference purpose. The general ( 1 ≠ 2 ) and resonant cases ( 1 = 2 ) are successively considered, for the sake of completeness and for future use. Generally, the used notation without the " " or " " subscripts indicates that the developed treatment is valid for both the TO and LO modes depending on the used Ω 2 value.
At 1 = 2 = 0, all parameters become real, so that the star added as a superscript to mark the imaginary character in Eq. (8) can be removed. The frequencies of the coupled modes, identifying with the eigenvalues of the relevant dynamical matrices, are ± 2 = 0 ± ( + 2 ) 1 2 , and the corresponding unit wave vectors take the general form As orthogonal unit vectors, | ± ⟩ can be written as, e.g., | + ⟩ = ( cos sin ) and | − ⟩ = ( sin −cos ). In this case, (cos ) 2 and (sin ) 2 conveniently represent the relative contributions of oscillators 1 and 2 to | + ⟩ in each symmetry (TO or LO), respectively. The same applies also to | − ⟩. Eventually (tan ) 2 represents the degree of mixing of the two oscillators in the coupled modes S16 . Besides, the unit vector defined as |2 ⟩ = ( sin 2 cos 2 ) = 1 √ 2 + 2 ( − ) is interesting as well since the ratio of its components, i.e., |tan 2 | = ⁄ provides a direct insight into the "strength of the coupling" (represented by ) depending on the proximity to the resonance between the uncoupled (TO or LO) oscillators S16 (governed by ). Basically the "strength of the coupling" is all the greater that (dictated by ′ ) is large and that is small (meaning that the resonance is close). Strictly at the resonance ( 1 = 2 = , being clear that is not the same for the TO and LO modes), where = 0, the real parts of the eigenvalues, corresponding to physical observable, express as 26 based on a first order Taylor expansion assuming ′ ≪ (verified experimentally with Zn~0.5Be~0.5Se -see below), with the usual condition on Ω 2 to distinguish between the TO or LO modes. As for the related wave vectors, they simplify to The mass displacements are the same in magnitude for oscillators 1 and 2, being either in the same or in opposite direction(s), i.e., in-phase or out-of-phase, corresponding to the so-called symmetric (SYM) and antisymmetric (ASYM) normal modes of vibrations of the coupled system, vibrating at frequencies + and − , respectively. Note that in the ASYM mode the mechanical coupling is not active; the corresponding spring ′ behaves in fact like a rigid bar connecting the two masses ( ), the reason why ′ does not contribute to − . In contrast ′ is "active" in the SYM mode, being at the origin of a finite frequency gap between the two coupled (TO or LO) modes. If we (virtually) neglect the change in when shifting from the TO to the LO modes, the upper LO frequency is shifted upward the lower TO one by an amount fixed by the ionic plasmon coupling (in reference to Ω 2 ), whereas the lower LO frequency matches the upper TO one (within the current approximation on ).
The diagonalization of the relevant TO (Ω 2 = 0) and LO (Ω 2 ≠ 0) dynamical matrices behind Eq. (15) leads to the complex set of (starred) eigenvalues 26 , with two variants, examined below, depending on the relative importance of the damping and coupling effects, reflected by the ratio. The two variants in question develop on each side of the exceptional point ( =1), where ∆= | ( + * ) − ( − * )| = 0 (see above).  > . : by assuming that all terms within the above bracket are small with respect to unity -which is valid for Zn~0.5Be~0.5Se (see below) -and by subsequently performing a first-order Taylor expansion (that is sufficient to keep the information on the -damping terms), one eventually arrives at providing information on the −dependence of the frequency gap between the coupled modes (with TO and LO types depending on the considered Ω 2 value).  < . : In this case the square root in Eq. (15) becomes purely imaginary. By repeating the above procedure and extending the Taylor expansion up to the second order (because the first order falls short of generating any dependence of the eigenvalues on the -damping terms), ∆ takes the form (17b) It is further instructive to determine the eigenvectors of the dynamical matrix, that coincide in fact with those of ̃, given by, i.e., complex ones, hence justifying the addition of a star as a superscript. At → 0, one recovers the SYM and ASYM normal modes. An actual displacement, i.e., a real one, is preserved for oscillator 2 as long as the coupling dominates over the damping ( > ). From the exceptional point onwards ( ≤ ), the displacement of oscillator 2 becomes purely imaginary, meaning that the latter overdamped oscillator is, in reality, frozen; only oscillator 1 vibrates, as sketched out in Fig. 1. The selective freezing of oscillator 2 at the exceptional point, applying as well in the TO and LO symmetries (using the relevant value in each case -see Sec. IIA1), is rather intuitive. Indeed, at this limit the coupling is exactly screened by the damping so that the original SYM and ASYM normal modes of the undamped system ( 1 = 2 = 0) representing the in-phase and out-of-phase motions of the two masses, respectively, merge into an unique mode with mixed SYM/ASYM character. The resulting degenerated normal mode has to achieve a balanced compromise between its two native normal modes, corresponding to one mass in motion and the other inert.
B. The Be-Se doublet of Zn~0.5Be~0.5Se : a high-pressure Raman study 1. Ambient pressure -combined TO/LO insight into the mechanical coupling ( ′ ) The pressure dependence of the BeSe-like TO and LO frequencies of Zn0.48Be0.52Se displayed in Fig.  S11b is discussed hereafter within the above damped model of coupled harmonic 1D-oscillators. The coupling can be either purely-mechanical (in reference to ′ ) or both electrical-mechanical (including on top of ′ ) whether considering the TO or LO modes, respectively. The LO-like -coupling is not an issue. It is determined by Ω 2 = 2 − 2 , whose pressure dependence for BeSe can be determined from existing data in the literature (detail is given below). This leaves ′ as the only unknown parameter governing the entire set of TO and LO frequencies in their pressure dependence.
A crude ′ -estimate can be achieved by assuming that ′ is not pressure dependent, and by placing the discussion at ambient pressure, i.e., far from the resonance ( , ). The justification is that at ambient pressure the two BeSe-like TO Raman peaks of Zn~0.5Be~0.5Se exhibit similar linewidths at full maximum ( 1 = 2 , Fig. S11a). Hence ≪ , meaning that the ′ −coupling is not yet challenged by overdamping of either mode. This is ideal for a direct ′ −insight. We anticipate that the mechanical coupling (in reference to ′ ) is weak, i.e., that ′ ≪ , since the two BeSe-like TO modes of Zn~0.5Be~0.5Se exhibit comparable Raman intensities at ambient pressure, as expected in absence of coupling in the ideal case of a random Zn⇿Be substitution S33 .
In fact, a combined (TO, LO) study is required to achieve a tentative ′ -estimate. Concerning the LO insight we refer more specifically to the lower/minor − − mode as explained below. One problem is that the latter feature is not visible in Fig. S11a, being screened by the dominant TO modes that emerge on each side of it. For a pure LO insight we resort to earlier Raman measurements done at normal incidence/detection onto the (100)-face of a ~1m-thick Zn~0.5Be~0.5Se/GaAs epitaxial layer, corresponding to a LO-allowed/TO-forbidden scattering geometry S38 . Generally, we have shown elsewhere that the TO and LO Raman modes detected with Zn1-xBexSe epitaxial layers and single crystals of similar compositions are remarkably similar (see Fig. 1 of Ref. S33), and can thus be treated on equal footing.
A two-step self-consistent (TO,LO) procedure is used to estimate ′ . The first step is concerned with the TOs. The ′ -dependence of the frequencies of the bare/uncoupled ( ,2 and ,1 , ranked in order of increasing frequency) TO modes (not observable experimentally) behind the experimentally observed ( ,− , ,+ ) Raman frequencies of the coupled TO modes detected with our Zn~0.5Be~0.5Se epilayer, used as setpoints, is derived for ′ varying continuously between 0 and 150 cm -1 (note that, in this case, the conditions ′ ≪ is fulfilled) using the TO-version of Eq. (8) implemented in absence of damping ( 1 = 2 = 0). For each ′ value one relevant ( ,2 , ,1 ) pair of frequencies is generated corresponding to theoretical ( ,− , ,+ ) frequencies matching the experimental values (marked by plain arrows) within ±0.5 cm -1 (the arbitrary set accuracy). We have checked that the same ( ,2 , ,1 ) pair is generated (within less than ~1.5 cm -1 ) for any given ′ value whether implementing the research procedure on the targeted ( ,− , ,+ ) values by incrementing (upward pointing open triangles) or by decrementing (downward pointing) the ( ,2 , ,1 )-test values from arbitrary sets of starting test frequencies. This provides confidence in the reported curves in Fig. S12. Remarkably the ( ,2 , ,1 ) vs. ′ curves (plain symbols) meet at ′~1 40 cm -1 , beyond which critical ′ value no ( ,2 , ,1 )-solution can be found. The next step is concerned with the LOs. The theoretical ( ,− , ,+ ) LO frequencies generated via the LO-version of Eq. (8) in absence of damping throughout the spanned ′ -domain by using the above ( ,2 , ,1 ) predetermined pairs as input parameters are shown in Fig. S12. Note that the asobtained theoretical curves in absence of mechanical coupling ( ′ =0) underestimate by far the experimental − − and − + Raman frequencies of the used Zn~0.5Be~0.5Se epilayer (pointed by external arrows). This overall discrepancy between experiment and theory concerning the LO frequencies has originally been attributed to a discrete fine structuring of the native TO modes behind the LOs, the result of inherent fluctuations in the local composition in a disordered system such as a mixed crystal S38 . In this case the transfer of available Be-Se oscillator strength mediated by the LO-like macroscopic electric field from the lower to the upper Be-Se sub-mode of the series, is both of intraand inter-mode types, and thus emphasized in comparison with a mere inter-mode transfer taking place in absence of fine structuring, with concomitant impact on the overall − + splitting, being emphasized. In fact, the − + shift cannot be explained by ′ , because increasing ′ softens + (Fig. S12). In contrast, ′ and fine-structuring work along for − , contributing both to its hardening. Therefore, an upper ′ estimate, useful to fix ideas, can be achieved by focusing on the − − shift and omitting the fine structure effect. In this approximation the perfect matching between the theoretical and experimental − − frequency is achieved for ′ =65 ± 20 cm -1 . The − − mode is overdamped in Zn1-xBexSe at any x value so that the − − frequency is marred by a large error S38 (refer to the dashed area in Fig. S12), with concomitant impact on the accuracy of the ′ value.
In a crude approximation we assume that ′ is not pressure dependent and transpose the study near the resonance (~590 cm -1 , ~15 GPa), corresponding to the actual crossing of the two BeSelike coupled TO modes, visible in Fig. S11b -within experimental uncertainty. As anticipated, the mechanical coupling is weak ( ′ ≪ ). The corresponding dependence of ∆ = | ( ,+ * ) − ( ,− * )| on at the resonance for the considered damped system of coupled BeSe-like TO modes, given by Eq. (17), is displayed in Fig. S13. An important feature dictated by ′ is the starting ∆ value at zero damping ( =0), currently falling into the range 3 -11 cm -1 , that fixes the overall shape of the admissible ∆ −domain (framed by dotted curves). The main feature is the exceptional point ( = ), corresponding to ∆ =0, as observed in the Raman spectra. Based on Fig. S13, ae are now in a position to discuss the pending issues (i-iv) on a quantitative basis. The source of overdamping ( ≠ 0) in our coupled system of two BeSe-like oscillators is the lower mode revealed by the gradual collapse of this mode when forced into proximity of the upper mode by pressure (Fig. S11a) -in reference to (ii), being clear that at ambient pressure such overdamping does not exist ( =0, since 1~2 ). The trend persists until a complete screening of the mechanical coupling ( = ) is eventually achieved at the resonance ( , ) -see Fig. S11b, hence characterized by an actual crossing of the two modes -in reference to (i). From this critical pressure onwards the coupled system of BeSe-like oscillators resonantly locks into its unique overdamped normal mode vibrating at the ~ frequency [see Eq. (11), in which ′ ≪ ] which keeps varying with pressure. The exceptional mode achieves a compromise between the distinct SYM and ASYM normal modes of the same-but-undamped system at the resonance (Sec. IIA2b). As such, it is characterized by the overdamped oscillator, i.e., the lower Be-Se one in our case, being inert/frozen, which nicely recollects with the ab initio insight -in reference to (iv). As for the particular value of the critical pressure ( ) corresponding to the resonance ( ) -in reference to (iii), it does not appear to be so remarkable in fact given the explanation provided in the main text. The only pending issue relates to the survival/death of the lower mode beyond .

Pressure dependence of the BeSe-like TO and LO Raman frequencies
What remains unclear from the experimental data at this stage is whether only the upper oscillator "survives" and the lower one is "killed" at the resonance -scenario 1, as predicted 26 (see Sec. IIA), or whether both modes survive as degenerated features into the same mode from onwardsscenario 2.
A decisive marker is the amount of Be-Se oscillator strength awarded to the exceptional mode ( ≥ ). In Zn0.5Be0.5Se the available amount of BeSe-like oscillator strength represents half the parent value at any pressure (feature 1) 8 , dictated by the Be content. This amount is equally shared between the two submodes forming (feature 2) the Be-Se doublet as long as these do not couple each other S38 . This is apparently the case at ambient pressure, reflected by the nearly equal Raman intensities of the two BeSe-like TOs (Fig. S11a). Scenario 1 or 2 applies depending on whether the exceptional mode carries the totality of the available Be-Se oscillator strength or only half of it, respectively.
By approaching the two BeSe-like TOs get closer and couple. The coupling presumably modifies the sharing of the available BeSe-like oscillator strength between the two modes meaning that the Raman intensities of the coupled TOs do not reflect any more the oscillator strengths of the underlying bare/uncoupled TOs.
In this case one may alternatively resort to the LOs, changing the focus from the Raman intensity to the Raman frequency then. In fact, in a pure zincblende compound such as BeSe, the oscillator strength monitors the magnitude of the TO-LO splitting of the unique phonon mode. The situation is not as simple with Zn0.5Be0.5Se since the Be-Se Raman signal is bi-modal. Additional complexity arises in that the polar (electrical-mechanical) LO modes couple very easily via their long-range electric field ⃗⃗ -in contrast with the non-polar (purely-mechanical) TO modes that need to be very close to develop a mechanical coupling (see above). As already mentioned (Sec. IIB1), the effect of the ⃗⃗coupling is to channel most of the available Be-Se oscillator strength towards a giant + feature, hence shifted at a high frequency far off its native TO doublet S38 -abbreviated (2) hereafter. In other words, the magnitude of the (2) − + splitting is directly monitored by the available amount of Be-Se oscillator strength at a given pressure, offering a valuable test for scenarios 1 and 2. Basically the (2) − + splitting will be large if + attracts the full amount of available BeSe-like oscillator strength at a given pressure -along scenario 2. In contrast, if one Be-Se oscillator freezes on mixing at the resonance -as predicted under scenario 1, half of the available Be-Se oscillator strength will be lost for the transfer to + , with concomitant impact on the magnitude of the (2) − + splitting, dropped by half with respect to scenario 2.
2-a. Scenario 1 vs. scenario 2: reference BeSe-like (TO,LO) data sets Useful sets of theoretical Zn0.5Be0.5Se TO and LO curves to test scenarios 1 and 2, displayed in Fig.  S14, to compare with experimental Zn0.48Be0.52Se TO (hollow symbols) and LO (full symbols) Raman frequencies taken from Fig. S11a (sample 1), comprises the following: (a) polynomial adjustments of the experimentally observed coupled TO frequencies; (b) corresponding bare/uncoupled TO frequencies ( ,1 , ,2 ) at ≤ ; (c) bare/uncoupled TO frequency of the exceptional mode at > ; (d) frequencies of the individual uncoupled LO modes at ≤ ; (e) Coupled LO frequencies ( −, , +, ) at ≤ ; (f) Frequency of the upper coupled mode LO mode ( +, ) at ≤ in its dependence on the phonon damping; (g)/(h) LO frequency of the exceptional mode considering that this attracts all/half the available BeSe-like oscillator strength.
Technically, the theoretical data sets (b-h) are generated as follows. The separate ( ,1 , ,2 ) frequencies of the bare-uncoupled TO oscillators at ≤ (b) are derived from the experimentally observed/coupled ( ,+ , ,− ) ones by using the undamped ( 1 = 2 =0) TO-version (Ω 2 =0) of Eq. (8) in case of a weak mechanical coupling ( ′ =65 cm -1 ≪ =590 cm -1 , see Figs. S12 and S14 for the ′ and estimates, respectively), as explained in Sec. IIB1. The ,1 = ,2 frequency of the uncoupled TO mode behind the exceptional TO mode at > (c) is derived on the same basis in absence of damping, by cancelling the square root term in Eq. (8). The individual frequencies of the uncoupled LO modes at ≤ , in reference to set (d), are obtained via the {− −1 ( )}-like form of the generic Raman cross section given in Ref. 19 using a truncated version of the relative dielectric function ( ) of Zn0.83Cd0.17Se, being reduced to the sole considered Be-Se oscillator as characterized by its coupled TO frequency, i.e., −, (any ) or +, . The nominal pressure-dependent (see above) amount of oscillator strength is preserved for each mode throughout the pressure domain. As for the individual phonon dampings ( 1 , 2 ) they have strictly no impact on the LO frequency (they only modify the broadening of the Raman peak -of no interest for our concern). The frequencies of the coupled LO modes displayed as set (e) are calculated along the same approach but by using the full expression of ( ) taking into account the two BeSe-like oscillators, as characterized by their coupled TO frequencies ( −, , +, ). This suffices to materialize the ⃗⃗ -coupling between neighboring individual LO modes. The individual phonon dampings play no role regarding set (e), as for set (d). The situation changes for the LO frequency of the upper coupled mode at ≤ , i.e., +, displayed as set (f). This is generated by injecting the uncoupled ( ,1 , ,2 ) to frequencies reported as set (b) into Eq. (8) taken in its LO version with the nominal pressure-dependent amount of available strength (Ω 2 ≠0) and parametrized with a weak mechanical coupling ( ′ =65 cm -1 ), further considering a finite pressuredependent damping ( 1 , 2 ≠0). In fact 1 is taken constant throughout the entire pressure domain (~20 cm -1 ), consistently with experimental observations (Fig. S11a) but 2 is pressure dependent. At ambient pressure 2 is minimal and matches 1 , testified by identical width at half height of the two BeSe-like TO Raman peaks (Fig. S11a). It roughly doubles (~35 cm -1 ) at the resonance ( , ) corresponding to the exact screening of the mechanical coupling by overdamping testified by the emergence of the "exceptional mode". The exact 2 value at this limit is derived from the ′ = correspondence for the current weak mechanical coupling ( ′ =65 cm -1 ). A linear dependence of 2 on pressure is further assumed, in a crude approximation. At > , the LO frequency of the exceptional mode, corresponding to set (g), is also calculated via Eq. (8) from which the square root term is omitted using the same relevant damping set at any pressure ( 1 =20 cm -1 , 2 =35 cm -1 ), considering that the exceptional mode is awarded the full amount of the pressure-dependent BeSe-like oscillator strength from onwards. The remaining set (h) refers to the same parameter obtained along the same line but on the basis of a dead loss of oscillator strength for the lower mode from onwards, meaning that the exceptional mode retains only half of the available BeSe-like oscillator strength.
In building up data sets (b-h) care is taken that most parameters coming into Eqs. (8) and (19) are pressure dependent, i.e., not only the frequencies , ( ) of the BeSe-like TO modes of Zn1-xBexSe, whether coupled or uncoupled depending on the used model (see above), but also several input parameters related to the end compounds, including , and , together with ∞, and 2-b. Discussion -experiment vs. theory In Fig. S12 the various predicted pressure dependencies of the − + frequency -referring to the data sets (d, e, f) -are superimposed onto the corresponding experimental data (full symbols), for comparison. Our guideline is that at ambient pressure, the experimental − + frequency stays well above any theoretical estimate -by as much as ~15 cm -1 , the result of natural fluctuations in the local Zn0.5Be0.5Se composition giving rise to a fine structuring of the two Be-Se TO sub-modes -see Sec. IIB1. The − + -shift is intrinsic to alloy disorder, and thus presumably not pressure dependent. Hence, it should persist as such throughout the entire pressure domain.
In fact, the − + -shift ~15 cm -1 between experiment and theory can be observed at high pressure only if the exceptional mode carries half of the available BeSe-like oscillator strength, meaning that only one sub-mode "survived" the resonance, as ideally expected under scenario 1. Somewhat ideally, the − + -shift stabilizes around ~15 cm -1 from onwards, meaning that the alternative submode is "killed" right at the resonance, i.e., on emergence of the "exceptional mode". For a tentative assignment of the active ("surviving") and passive ("killed") submodes involved in the exceptional mode beyond we resort to the TOs. The pressure dependence of the exceptional TO mode at ≥ is in continuation of that related to the upper mode at < . Besides, the progressive collapse of the lower sub-mode with increasing pressure at < is a precursor sign of its full extinction at . On this basis, the active and passive TO oscillators behind the exceptional mode post resonance can be traced back to the upper and lower ones ante resonance, respectively.
However, the actual "freezing" of part of the available oscillator strength above makes no physical sense. The "freezing" must be apparent only. In fact, we have checked that the TO sub-mode given up for "dead" beyond is "revived", i.e., regains its original oscillator strength, when the pressure drops below in a downstroke Raman experiment (pressure decrease). Our present view is that when the lower mode is forced in the proximity of the upper mode by pressure, it "evades" an effective coupling by becoming overdamped right at the resonance. By doing so, the lower mode retains its original oscillator strength -though in an overdamped form, hence turned away from the inherent transfer of oscillator strength accompanying an actual coupling with the upper mode.
It is interesting to examine in detail how the "2-mode⇾1-exceptional-mode" transition develops on approach to . In absence of damping, the (2) − − + splitting is expected to drop suddenly by half when the two distinct Be-Se sub-modes ( < ) resonantly lock into the exceptional mode ( > ) -compare the data sets (e) and (h). Such sharp transition opposes to experimental findings, indicating a smooth transition (full symbols). Now, the absence of damping is unrealistic since the overdamping is the sine qua non condition for the emergence of the exceptional mode (Sec. IIB). In fact, by incorporating damping in the two-mode regime ( < ) -in reference to the data set (f), the − + mode tends to soften already close to ambient pressure, and the softening progressively increases with pressure until coincidence with the − + frequency of the exceptional mode exactly at the resonance ( ) -at the origin of the data set (h), as ideally expected.
Generally, the current validation of scenario 1 based on a combined understanding of the TO and LO Raman data in the Be-Se spectral range of Zn1-xBexSe reveals that the so-called "exceptional point" of a coupled system of damped harmonic (1D-)oscillators is not a purely theoretical feature but can be observed experimentally.
Last, it is worth to mention that, given the ′ (~65 cm -1 ), , (~501 cm -1 ) and , (~450 cm -1 ) values, the coupling between the polar LO modes mediated by their common macroscopic electric field remains quasi unaffected by overdamping ( ≫ , Sec. IIA1), though this suffices to bring the system of non polar (purely mechanical) TO modes at its exceptional point ( = ).

Figure S2
 Probability for B-C percolation on the zincblende and wurtite A1-xBxC lattices depending on clustering. Probability for wall-to-wall B-C percolation in large (10×10×10) A1-xBxC supercells with zincblende (hollow symbols) and wurtzite (full symbols) structures -corresponding to different 1-2-3-1… and 1-2-1… sequences of high-density (111)-type packing planes (in the zincblende case) from top to bottom -in the ideal case of a random A⇿B substitution (~0, at any x) and in case of a pronounced trend towards local clustering (~0.5, at x=0.17). Both types of atom arrangement are optimized by simulated annealing (see Methods). Side and front views of a B-C percolative path -emphasized (grey scale) -in the zincblende lattice, with a distinction between like substituents (B) from the bottom (-) and top (+) planes, for clarity.

Figure S3
 High-pressure X-ray Zn0.83Cd0.17Se diffractograms. Selection of high-pressure Zn0.83Cd0.17Se powder X-ray diffraction diffractograms taken in the upstroke (↑) regime with the 0.378 Å radiation showing the phase transition sequence from zincblende (ZB) to rock-salt (RS). The reported diffractograms cover successively the pure zincblende (ZB) phase, the progressive emergence of the rock-salt (RS) phase, the disappearance of the zincblende phase and the pure rock-salt phase, from bottom to top. The final diffractogram obtained at nearly ambient pressure at the term of the downstroke (↓) regime is added (bottom curve), for reference purpose. Circles and stars mark diffraction lines due to Au used for pressure calibration and Neon used as the pressure transmitting medium, respectively. 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 2 theta (degree)

Figure S5
 Composition dependence of Zn1-xCdxSe structural/mechanical parameters. Bulk modulus at ambient pressure of Zn1-xCdxSe taken in the (dominant) zincblende phase (B0, left axis) and Zn1-xCdxSe zincblende⇾rock-salt pressure transition (right axis) in the upstroke regime. The average B0 values (circles) derived from the current high-pressure X-ray data (full symbols, in reference to Fig. S4) and by applying the same procedure to the ZnSe data taken from Ref. S13 (hollow symbol) are marred by error bars extending up/down to extreme B0 values, as indicated. The transition pressure is identified as the mean value between the critical pressures corresponding to first emergence of the rock-salt phase and subsequent disappearance of the zincblende/wurtzite phase in the upstroke regime. The related error bar is defined accordingly. 42. The fundamental optical band gap of Zn0.83Cd0.17Se at 0 GPa corresponding to the onset of absorption in the ellipsometry data is indicated, for reference purpose. By exciting the Raman spectra with the 488.0 and 514.5 nm laser lines (the hatched areas cover ~200 cm -1 , of the order of the detected PP frequencies - Fig. 2) in the used Stokes geometry (corresponding to < , see arrows) the addressed spectral ranges fall close to the gap-related singularity in the dispersion of the refractive index throughout the studied pressure domain.

Figure S9
 Ab initio Zn1-xCdxSe PhDOS depending on pressure. Phonon density of states (PhDOS) calculated at ambient (0 GPa, thin lines) and high (10 GPa, thick lines) pressure by applying the AIMPRO ab initio code to large (216-atom) disordered (~0) Zn1-xCdxSe zincblende-type supercells spanning the composition domain. Similar supercells are used at x~0.3 and x~0.7, by merely inverting Zn and Cd. Figure S10  Comparative ab initio insight into the Zn~0.5Cd~0.5Se and Zn~0.5Be~0.5Se bond length distributions. Bond length distributions at ambient pressure related to similar 216-atom disordered (~0) X~0.5Zn~0.5Se zincblende-type supercells (X=Cd or Be) after full relaxation (of the lattice constant and of the internal atom positions) achieved by using the AIMPRO ab initio code. a. X=Cd. b. X=Be. Both supercells are identical except that the sites occupied by Cd in one supercell are occupied by Be in the other one (as sketched out). The X-and Zn-substituting sites are distinguished in the depicted generic supercell, for clarity.   Fig. 1 therein). The experimental ,− frequency, though marred by a rather large error bar (shaded area), helps to estimate ′ (as schematically shown).

Figure S13
 Exceptional phonon point of Zn0.5Be0.5Se. Frequency gap between the TO-like SYM. and ASYM. normal modes at the resonance depending on competition between mechanical coupling ( : fixed by ′ ) and overdamping ( : depending on 1 vs. 2 ), as emphasized (shaded area). At exact compensation between gain (coupling) and loss (overdamping) the phonon exceptional point is achieved corresponding to degeneracy of the coupled TOs (dark spot).

Figure S14
 Pressure-dependence of the Zn~0.5Be~0.5Se Raman frequencies -Theory vs. experiment. Experimental TO (hollow symbols) and LO (full symbols) Zn0.48Be0.52Se Raman frequencies depending on pressure (Fig. S7). a Polynomial adjustments of the experimental TO frequencies. b Bare/uncoupled TO frequencies ( ≤ ). c Bare/uncoupled TO frequency of the exceptional mode ( > ). d Uncoupled LO frequencies ( ≤ ). e Coupled LO frequencies ( ≤ ). f Coupled +, frequency obtained by considering a progressive overdamping of the lower oscillator until the exceptional point is achieved at the resonance ( , ). g LO frequency of the exceptional mode being awarded the full amount of Be-Se oscillator strength. h Corresponding LO frequency in case of a dead loss of oscillator strength for the lower mode from the resonance onwards.