Introduction

Lattices of magnetic ions having regular triangular coordination are characterized by multiple ordering phenomena including ferromagnetism, frustrated antiferromagnetism, density waves and superconductivity (SC). These lattices attracted a lot of attention not only for the magnetism but also for the specific band structure being characterized by a Dirac dispersion and Weyl nodes induced by spin-orbit coupling. As a typical example, the vanadium-antimony compound class AV3Sb5 (A =  K, Rb, Cs) forming a Kagome lattice with alternating hexagons and triangles was discovered recently1,2,3,4. The V-Sb Kagome layers are separated by Sb honeycomb-like layers and alkali monolayers as shown in Fig. 1a. At low temperature, charge density waves (CDW) and SC may occur. The focus here is placed on the CDW transition forming a 2 × 2 × 2 superlattice at TCDW in the 100-Kelvin range which may be driven by an unconventional mechanism beyond electron–phonon interaction. Rather, the proximity to a Van Hove singularity close to the Fermi surface is considered responsible for the instability5.

Fig. 1: Structure and polarization configurations in CsV3Sb5 with the related Raman vertices.
figure 1

a The crystal structure. Cs, V, and Sb atoms are shown in green, blue and yellow, respectively. b, c Kagome lattice of the V-Sb layers. The polarization configurations of A1g and E2g symmetries are superimposed as blue and red circular arrows. The Raman vertices are shown with the colour mapping for the d first- and e second-order A1g symmetry, f, g first-order E2g symmetry. The first Brillouin zone is represented by the black hexagon. The dark blue (electron-like pocket α), red (hole-like pocket β), orange (hole-like pocket γ) and cyan (electron-like pocket δ) curves indicate the Fermi pockets. The green arrow in (d) illustrates the ordering vector Q. The dashed lines in (d) indicate the corresponding folded Brillouin zone.

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Obviously, the ordering vector Q connects Γ and M points (see the green arrow in Fig. 1d), in agreement with the electronic structure predicted theoretically6 and observed by angle-resolved photoemission spectroscopy (ARPES)7 and scanning tunnelling spectroscopy (STS)8. Yet, the meaning of the observed energy scales is still controversial. ARPES9 and STS10,11 find a gap at 20 meV and thus just one-fourth of the scale observed by infrared spectroscopy12,13. More recent ARPES measurements disclose that the small gap may originate from massive Dirac points14, and a larger CDW gap may open at the M points14,15 and corresponds to a ratio 2Δ/kBTCDW ≈ 20 far beyond the weak coupling prediction of 3.53. Complementary to spectroscopic methods thermodynamic studies indicate a divergence in the heat capacity being more compatible with a first-order rather than a second-order transition as usually expected for a CDW2.

There are various experimental methods that can be used to attack this issue. One may look for anomalies close to the ordering vector Q in the acoustic phonon branches using either neutron16 or inelastic X-ray scattering5. This search has been unsuccessful so far, and the conclusion reached is that either k-dependent electron–phonon coupling or electron-electron interaction is the origin of CDW ordering. Alternatively, optical phonons displaying renormalization effects at TCDW17,18,19 or Fano-type line shapes may indicate strong electron–phonon coupling. In addition to phonons, oscillations of both the amplitude and the phase of the order parameter are expected for a CDW system20. For symmetry reasons, Raman scattering and time resolved techniques project the amplitude mode (AM) directly thus tracking the CDW phase transition18,19,21,22,23. In weak-coupling systems, the AMs are expected to have a symmetric Lorentzian line-shape21,23 with increasing width upon approaching TCDW from below. It is not clear which effect on the AM may be expected if the coupling increases substantially. Finally, the CDW electronic gap is accessible by light scattering.

In this paper, we address the open questions as to the states involving the formation of CDW order, including the size and momentum dependence of the electronic gap, the renormalization of phonons, and the evolution of collective modes, by investigating the temperature and polarization dependent inelastic light scattering response in CsV3Sb5. In particular, in contrast to the AMs found in other well-known CDW materials, we observe the A1g AM to be asymmetric in CsV3Sb5, exhibiting a strong Fano resonance. These results along with the strong anharmonic decay of the two prominent Raman-active phonons and most of the CDW-induced phonons highlight the importance of a cooperation between strong phonon–phonon and electron–phonon coupling in the formation of CDW in CsV3Sb5.

Results

Electronic continuum

Figure 2 shows the A1g and E2g Raman spectra of CsV3Sb5 in the range from 50 to 3600 cm−1 above and below TCDW. There is a symmetry-dependent redistribution of spectral weight from below to above the intersection points at approximately 1400 ± 50 and 1540 ± 50 cm−1 in the E2g and the A1g spectra, respectively, which was not reported before. The redistribution of the spectral weight is well reproduced for different laser energies (see Supplementary Materials C for details). There is no sharp onset, rather the spectra are continuous similar to earlier observations in 2D CDW systems24.

Fig. 2: CDW gap excitations in both A1g and E2g symmetry.
figure 2

a, b Raman response above and below TCDW in A1g and E2g symmetry. The redistribution of the spectral weight is highlighted by the cyan areas. The insets show the difference between spectra at 124 K and the low-temperature spectra, with temperature indicated by the colour bars on the right. The small and large gap features are indicated by the red vertical arrows. c The FS-integrated electronic response is calculated from DFT using the pristine (orange), Star of David (SoD, black), and inverse Star of David (iSoD, violet) lattice. The loss and gain of intensity between the response in the pristine and iSoD-distorted lattice are highlighted by cyan areas. In agreement with the experimental results, the small and large gaps are also reproduced by DFT calculations (marked by the red arrows). Insets: The SoD and iSoD distortion in the V-Sb layer. The blue shaded area shows the pristine unit cell. The unit cell below TCDW is twice as large.

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Upon warming the amplitude of the redistribution decreases and disappears completely above TCDW as shown in the insets of Fig. 2a, b, where we plot the difference between the spectra measured slightly above TCDW and those below. The difference spectra reveal additional features close to 600 cm−1 (75 meV) and 450 cm−1 (56 meV) for A1g and E2g symmetries, respectively, and suggest that the high-energy part of the E2g spectra consists of two distinct temperature-independent structures at 2100 ± 200 and 3000 ± 200 cm−1, whereas there is only a board peak at 2500 ± 200 cm−1 in the A1g spectra (large gap).

Along with the experiments we performed DFT simulations as presented in Fig. 2c. The joint density of states (see Methods and Supplementary Materials G for more details) is determined for the pristine lattice and for the two distortions (see the insets of Fig. 2c) allowed by symmetry below TCDW. For the tri-hexagonal (iSoD) distortion the reduction in spectral weight below 2000 cm−1 is bigger than for the SoD case, where the effects of the distortion can barely be seen. Thus, the electronic Raman spectra favour the same distortion as the analysis of phonon instabilities19. In addition, in agreement with experimental observations, large and small gap features are clearly identified. The mismatch in energy between the DFT calculations and the experiments may be reconciled by considering a renormalization factor of ~1.67 to be expected for the band energies in this material class having strong electronic correlations25.

Phonons and amplitude modes

Two prominent Raman-active phonon lines are observed saturating at 137.5 and 119.5 cm−1 in the zero-temperature limit for A1g and E2g symmetry, respectively, as shown in Fig. 3. They have previously been identified by Raman scattering17,18,19,26. Both the A1g and the E2g phonon show weak but significant renormalization effects at TCDW (see Fig. 3). Upon cooling, the A1g phonon changes discontinuously near TCDW and saturates below (see Fig. 3b). Although the energies observed upon cooling and heating do not exactly coincide the hysteresis cannot be considered significant enough to support a first-order phase transition as suggested by the thermodynamic data27. The energy of the E2g line does not exhibit significant changes across TCDW (see Fig. 3f). A weak dip exactly at TCDW may exist but our resolution is not sufficient here. In either symmetry, the line widths exhibit kinks at TCDW and decrease faster below TCDW than above (see Fig. 3c, g). The line widths are well described in terms of symmetric anharmonic decay (full lines in Fig. 3c, g)28. The resulting phonon–phonon coupling constants λph-ph are substantially enhanced below TCDW.

Fig. 3: Phonon renormalization at TCDW.
figure 3

a, e The temperature evolution of the A1g and the E2g phonon lines was measured at 9, 25, 45, 55, 65, 75, 80, 85, 89, 95, 99, 124, 154, 203, 253, 302 K, respectively. For clarity, the spectra measured above 9 K are consecutively offset by 15 cts/(s mW). b, c, f, g Phonon energies ωph widths (FWHM) of the two lines are derived from Voigt fits (see “Methods”). b A hysteresis may exist below TCDW. The green line is derived from the volume expansion27 using Grüneisen theory with γ = 2.45. It is adjusted to the blue data points. d Zoom in on the range near TCDW of the energy (b). The shaded area indicates a range of 10 K, where the A1g phonon exhibits a dip and an increase of ωph above TCDW. f The temperature dependence of the energy in E2g symmetry is weaker than for the A1g mode in (b), and the related Grüneisen parameter is thus smaller, γ = 1.65. There may be an anomaly directly at TCDW. c, g Temperature dependences of the phonon line widths (ΓL) of the A1g and the E2g phonons. The data were fitted separately below and above TCDW using an anharmonic model28 (see Supplementary Materials E for details). There are obvious slope changes at TCDW for both the A1g and the E2g phonons. h Volume expansion coefficient αV(T). The error bars include the statistical and systematic errors from the fitting of the phonon lines and the reproducibility of the spectrometer.

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Along with the measured phonon energies we show their variation with temperature expected from the volume contraction according to Grüneisen theory29 (full lines in Fig. 3b, f) using the thermal expansion data of ref. 27 (more details can be found in Supplementary Materials E). The Grüneisen parameters γi for the A1g and the E2g phonon are found to be 2.45 and 1.65, respectively, close to the typical value of 2. The expansion data confirm that the transition at TCDW is weakly first order since the volume is not constant across TCDW. The anomaly of the expansion coefficient αV(T) is substantial (Fig. 3h), but the volume expansion is small27 and the effect on the phonon energies, for which αV(T) is used, is even smaller. While describing the data well for T > TCDW, the volume change cannot explain the hardening of approximately 1.2 cm−1 of the A1g phonon at TCDW. Rather, it predicts a small softening of the phonon frequency. On the other hand, the hardening of the A1g phonon is properly predicted by our DFT simulations (Details can be found in Table II of Supplementary Materials G). Zooming in on the region around TCDW, a precursor of the phase transition is resolved in a range of approximately 10 K above TCDW (see Fig. 3d).

The weak additional lines observed below TCDW are indicated by black asterisks and orange diamonds in Fig. 4a and b. In the zero-temperature limit the three A1g lines are located at 43.0, 105.4 and 200.0 cm−1. The six E2g lines appear at 43.2, 60.0, 101.0, 180.0, 208.2 and 224.0 cm−1. The lines at 43.0 and 105.4 cm−1 are also found in pump-probe experiments30,31. These emerging lines are observed at nearly the same energies for different laser excitations (see Supplementary Materials D for details). Details of the temperature-dependent positions and widths of these lines can be found in Supplementary Materials E.

Fig. 4: Zone folded phonons and amplitude mode in CsV3Sb5.
figure 4

a, b Raman spectra of CsV3Sb5 below and above TCDW in A1g and E2g symmetry. Below TCDW, several additional peaks appear which are marked by black asterisks for the zone folded phonon lines and orange diamonds for the amplitude modes. c, d Temperature-dependent Raman spectra of CsV3Sb5 in A1g and E2g symmetry, respectively. For clarity, the spectra are consecutively offset by 0.5 cts/(s mW) each except for those measured at 9 K.

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The lines marked by asterisks have weak and conventional temperature dependences and soften by less than 2% between the low-temperature limit and TCDW (see Fig. 4c, d). The lines at 105 and 208 cm−1 labelled with orange diamonds shift to lower energies by 17 and 10 cm−1, respectively, upon approaching TCDW, corresponding approximately to 15% and 5% relative shift. These two lines are identified as CDW AMs in CsV3Sb5. The A1g line broadens by approximately an order of magnitude close to TCDW and assumes a rather asymmetric shape in the range 40–80 K (see Fig. 5a).

Fig. 5: Asymmetry of the A1g amplitude mode.
figure 5

a Temperature evolution of the A1g AM. Except for the spectrum at 9 K, the spectra have been consecutively shifted by 1.5 cts/(s mW) for clarity. The Fano fits are superimposed in the spectra (light grey lines). b Top panel: The comparison between a superposition of two Lorentzian lines as suggested in ref. 18 and a Fano line shape to the A1g AM. The Fano line yields a better residuum R2. Results for the entire temperature range are presented in Supplementary Materials H. Bottom panel: The deviation of the spectra from the fitting curves (Red line: Fano, blue line: two Lorentzians). c The asymmetry parameter 1/∣q∣ as a function of normalized temperature in CsV3Sb5. The error bars are estimated from the fitting of the AM lines. d The temperature dependence of AM energies in various CDW materials. The data points in grey and black were extracted from refs. 23,24,40,41,50. The peak energies of both AMs obviously deviate from the prediction of mean field theory (red curve) in CsV3Sb5. S1 and S2 in (c) and (d) denote two different samples.

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Discussion

In the following electronic excitations, phonon anomalies and collective amplitude modes (AMs) below the ordering temperature TCDW will be discussed.

Excitations across the gap

The redistribution of the spectral weight below TCDW displaying slightly different intersection points and peak positions in the electronic A1g and E2g spectra (see Fig. 2) indicate anisotropies of the energy gap. The resistivity shows that the system remains metallic below TCDW and that the gap vanishes on extended parts of the Fermi surface. In contrast to a superconductor, where the gap opens symmetrical with respect to the Fermi energy EF at ± k, single- and two-particle spectroscopies cannot readily be compared in a CDW system. While both Raman and IR spectroscopy measure occupied and unoccupied states, thus the joint density of states with specific weighting factors, ARPES probes only the occupied states and STS either tunnels into unoccupied states or extracts electrons from occupied bands. This fact manifests itself directly in the asymmetry of the STS spectra for negative and, respectively, positive bias8. Yet, in all spectroscopies, two distinct features are observed at low and high energies. For two-particle techniques, the related features are expected at approximately twice the energy observed by single-particle methods.

In systems having strongly momentum-dependent gaps, the gap energy is closer to the intersection points than the peak energies of the Raman spectra. The resulting magnitude of the larger gap Δ> is then at approximately 88–96 meV yielding a gap ratio of 2Δ>/kBTCDW in the range 21–23. Presumably due to the different projections of IR and Raman the results of the optical conductivity peak at an energy slightly below those of Raman spectroscopy13. As opposed to the IR results, we do not observe significant temperature dependences of neither the intersection points nor the peak energies.

In ARPES, gap features are extracted from the symmetrized spectra of CsV3Sb5 and KV3Sb57,14,15. Large gaps are found on the smaller FSs around the K points of the BZ (γ and δ bands in the notation of ref. 15) with the maxima reaching Δ> ≈ 80 meV close to the M points. It is also reproduced by our DFT calculations at M point (see Supplementary Materials G for details). These gaps are slightly smaller than those derived from the Raman spectra of CsV3Sb5. One possible reason are the final states into which the electrons are scattered. In ARPES electrons propagate into the vacuum whereas in Raman they are scattered into unoccupied states above EF. The selection rules are likely at the origin of the differences between A1g and E2g.

In addition to the large gaps, there are also small gaps around the M points having energies close to Δ< ≈ 20 meV15. The small gaps open along the Γ-K line in our DFT simulation (see Supplementary Materials G for details). We identify the Raman peaks at approximately 500 cm−1 with the smaller gaps although the single-particle gaps derived from Raman scattering, Δ< ≈ 30 meV, are still too large. As a matter of fact, comparing energy scales in a CDW systems is not as straightforward as in a superconductor because of missing the particle-hole symmetry. On the other hand, one may learn a lot on the unoccupied states after a successful implementation of the selection rules in both Raman and IR. Yet, this endeavor requires an in-depth understanding of interband scattering which is still missing32.

Persistent phonons

The two phonon lines of the pristine structure persist in the distorted phase below TCDW. There are changes at the transition in both the positions and the widths of the lines. The widths are described successfully in terms of anharmonic decay into two acoustic modes having momentum ± k28 as shown in Fig. 3c, f. There is a remarkable change of slope at TCDW which goes along with an increase of the phonon–phonon coupling λph-ph by a factor of ten and three for the A1g and the E2g line, respectively. The enhanced coupling constants in the CDW phase suggest that the ph–ph coupling is not directly mediated by anharmonicity but by electron–phonon interaction which increases upon approaching TCDW when the gaps close.

Above TCDW, the modes’ energies are well described by the volume change using Grüneisen theory. Below TCDW, only the E2g line obeys this prediction while the energy of the A1g phonon changes by 1.2 cm−1 when the zero-temperature values are compared. The energy change of the A1g mode is a result of the new positions of the V atoms below TCDW. It was shown that only the iSoD distortion removes the negative energies of the acoustic phonons19. Along with this DFT result and our own simulations for the electronic Raman spectra we conclude that the iSoD distortion is more likely. The phonon energies derived from our DFT simulations (see Supplementary Materials G, Table II) yield the same shift for both distortion patterns. On the basis of symmetry arguments we cannot distinguish between SoD and iSoD either since both belong to the same symmetry group. Similarly, we are not in a position to comment on possible stacking sequences along the c-axis as suggested by X-ray studies33,34.

New phonon lines below T CDW

The additional phonon lines below TCDW result from the lowering of the lattice symmetry as spelled out by Wu et al.18 and Liu et al.19. The lattice distortion folds the phonon dispersion by a wave vector Q that links the Γ and M points as seen in Fig. 1d. Here, the phonons at the zone boundary are folded to the Γ point and become Raman active35,36. If one considers a SoD or an iSoD distortion (see the insets of Fig. 2c) expected for CsV3Sb5 (refs. 5,11,37), the V atoms move from the 3g (1/2, 0, 1/2) to 12q (x, y, 1/2) Wykoff positions, and one expects eight additional Raman-active modes (two in A1g, four in E2g and two in E1g). This figure matches the number of the new phonons in our measurements (asterisks only). Furthermore, most of the zone-folded modes quantitatively match the frequencies obtained in DFT simulations when considering the iSoD distortion19. The new lines have similarly large phonon–phonon coupling constants λph-ph as the strong lines appearing above and below TCDW (see Fig. 3d, f and Table I in the Supplementary Materials E), indicating strong phonon–phonon coupling.

Amplitude modes

The lines at 105 and 208 cm−1 in A1g and E2g symmetry, respectively, have significantly stronger temperature dependences than the other lines appearing below TCDW and are identified as AMs. Yet, the variation is much weaker than predicted by mean-field theory (see Fig. 5d) and observed for the tritellurides, e.g., refs. 23,24. There may be various reasons for the deviations: (i) Impurities lead to a saturation of the AM frequency at approximately the impurity scattering rate38. Here, this would imply a rather disordered system with an electronic mean free path of only a few lattice constants. (ii) An effect of strong electron–phonon coupling seems more likely, although enhanced coupling does not necessarily entail a deviation from mean-field theory. Since Ginsburg-Landau theory18 is applicable only close to the transition, where no data are available, the study of an extended temperature range below TCDW may be deceptive. In addition, the AM is not directly related to the gap, where single-particle (STS, ARPES) and two-particle (IR, Raman) results may return significantly different results, but rather to a soft mode above TCDW. (iii) Strong phonon–phonon coupling and, consequently, higher order contributions from the phonons are not unlikely since the coupling λph-ph of all modes below TCDW is substantial (see Fig. 3c, g as well as Table I in Supplementary Materials E). This effect is predicted to enhance 2Δ/kBTCDW substantially and induce deviations from the mean-field temperature dependence of the AMs39. As mentioned above the enhanced phonon–phonon coupling is most likely mediated by a substantial electron–phonon coupling entailing the asymmetry of the A1g amplitude mode.

The anomalies of the A1g line at 105 cm−1 are incompatible with conventional phonons. Right below TCDW the line width is as large as 50 cm−1 (more details can be found in Supplementary Materials E). Previously the asymmetry has been interpreted in terms of two superimposed lines having individual temperature dependences18 or a hybridisation with CDW-induced lines19. We did not observe a double structure at low temperature for any of the three excitation energies studied (see Supplementary Materials D) but rather a narrow, yet asymmetric, line having a width (FWHM) of approximately 6 cm−1 at 8 K. We tested both hypotheses and found the Fano line to reproduce the data better in the entire temperature range (see Fig. 5b). For describing the mode we used the simplified Fano formula where the line width Γ is much smaller than the resonance energy ωAM, and 1/∣q∣ is the asymmetry parameter,

$$I(\omega )=\frac{{I}_{0}}{| {q}^{2}+1| }\frac{{(q+\varepsilon )}^{2}}{1+{\varepsilon }^{2}};\quad \varepsilon=2\frac{\omega -{\omega }_{{{{{{{{\rm{AM}}}}}}}}}}{\Gamma }.$$
(1)

The description in terms of a Fano shape yields monotonous temperature dependences of both width and resonance energy whereas the superposition of two Lorentzian lines yields erratic temperature variations as shown in Supplementary Materials H thus favoring a Fano resonance as the origin of the asymmetric amplitude mode. 1/∣q∣ becomes maximal at 68 K where the transition from 2 × 2 × 2 to 2 × 2 × 4 stacking is observed by X-ray diffraction33 (see Fig. 5c). The decrease of 1/∣q∣ towards zero temperature is a result of the opening of the CDW gap below 1500 cm−1 which reduces the continuum (see Fig. 2a). The Fano shape of the AM is unique in CsV3Sb5 and has not been observed in other well-known CDW materials, such as ErTe324, LaTe323, 2H-TaSe240 or K0.3MoO341, where all AMs have a symmetric Lorentzian line-shape (See Supplementary Materials I).

The asymmetric AM, along with the missing soft mode behaviour in the acoustic branches5,16, the large 2Δ/kBTCDW ratio, and the weakly first-order phase transition argue against the weak-coupling picture. In addition, we derive signatures of strong phonon–phonon coupling from the anharmonic decay of the majority of the Raman-active optical phonons (see Fig. 3c, g and Supplementary Material E), proposed by Varma and Simons as an important ingredient for strong coupling39. These observations supplement earlier work and highlight the interrelation of various interactions conspiring to drive the CDW.

Usually one argues that strong fluctuations suppress TCDW in systems having a large gap. In some materials such as ErTe3 electronic fluctuations can directly be observed24 above TCDW. ErTe3 is in fact a very clean compound and may therefore be considered a textbook example. Yet, it seems unlikely that impurities alone can explain the absence of fluctuations in CsV3Sb5 (see Supplementary Material F for details). The phonon anomalies close to TCDW (Fig. 3d) could indicate a narrow fluctuation regime similar to the one- or two-Kelvin range above the magnetic transition in MnSi42.

In summary, we performed a polarization- and temperature-dependent Raman scattering study of the Kagome metal CsV3Sb5. The electronic continua in both the A1g and E2g symmetry exhibit a spectral-weight redistribution below the charge-density-wave transition temperature, TCDW ≈ 95 K. This redistribution indicates an energy gap of 2Δ ≲ 1 500 cm−1 (185 meV) corresponding to 2Δ/kBTCDW close to 22. In addition, we observe features in the range 500 cm−1 (60 meV). These magnitudes correspond qualitatively to the distinct single particle gaps Δ< ≈ 25 meV and Δ> ≈ 80 meV observed by ARPES14,15. The DFT calculations reproduce the spectral weight redistribution favouring an iSoD distortion for T → 0. In the low-energy part of the spectra several phonons pop out below TCDW in addition to the two modes in A1g and E2g symmetry Raman active at all temperatures. The additional lines are related to the lattice distortion due to the CDW transition. Intriguingly, we identified two CDW amplitude modes having energies of \({\omega }_{{{{{{{{\rm{AM}}}}}}}}}^{A1g}=105\) cm−1 and \({\omega }_{{{{{{{{\rm{AM}}}}}}}}}^{E2g}=208\) cm−1 in the low-temperature limit. The A1g AM couples strongly to a continuum as indicated by the Fano-type line shape displaying the strongest asymmetry at the putative cross-over temperature of ~60 K between 2 × 2 × 2 to 2 × 2 × 4 ordering33. The mode’s temperature dependence is weaker than predicted by mean field theory. This discrepancy may result from either impurities38 or strong coupling39. Since the crystals are well-ordered we consider the strong-coupling scenario including anharmonic phonon–phonon and electron–phonon coupling39 more likely. This interpretation is consistent with the large electronic gap and the asymmetric AM. Thus, the cooperation of mode-specific electron–phonon and intermediately strong phonon–phonon coupling may be more likely a route to the CDW transition in CsV3Sb5 than, e.g., nesting.

Methods

Samples

Single crystals of CsV3Sb5 were grown from liquid Cs (purity 99.98%), V powder (purity 99.9%) and Sb shot (purity 99.999%) via a modified self-flux method43. The mixture was put into an alumina crucible and sealed in a quartz ampoule under argon atmosphere. The mixture was heated at 600 °C for 24 h and soaked at 1000 °C for 24 h, and subsequently cooled at 2 °C/h. Finally, the single crystals were separated from the flux by an exfoliation method. Apart from sealing and heat treatment procedures, all other preparation procedures were carried out in an argon-filled glove box. The crystals have a hexagonal morphology with a typical size of 2 × 2 × 1 mm3 and are stable in the air. The sample used for the Raman experiments has a TCDW of 95 K, characterized by resistivity and in-plane magnetic susceptibility (see Supplementary Materials A for details).

Light scattering

The inelastic light scattering experiments were preformed in pseudo-backscattering geometry. The samples were mounted on the cold finger of a 4He flow cryostat immediately after cleaving. For excitation, a solid-state and an Ar+ laser emitting at 575, 514, and 476 nm were used. In the experiments, the laser power was adjusted to maintain an absorbed power of Pabs = 4.0 mW, resulting in a heating rate of 0.5–1 K/mW. The inelastic spectra were divided by the Bose factor yielding Rχ″(Ω, T) = π{1+n(Ω, T)}−1S(q ≈ 0, Ω) where χ″ is the imaginary part of Raman response function, R is an experimental constant, and S(q ≈ 0, Ω) is the dynamical structure factor44. Typical phonon lines are described by Lorentzians. If the width is close to the spectral resolution or below a Voigt function (convolution of a Lorentzian and a Gaussian, where the Gaussian width is set at 4.3 cm−1) has to be used.

For projecting the A1g and E2g symmetries RR and RL polarization configurations were used, respectively. In terms of perpendicular linear polarizations x and y, R and L are given by \(R=\frac{1}{\sqrt{2}}(x+iy)\) and \(L=\frac{1}{\sqrt{2}}(x-iy)\), respectively. The configurations with respect to the Kagome plane are shown in Fig. 1b, c. For electronic Raman scattering the form factors are important and highlight parts of the Brillouin zone. The form factors or Raman vertices may be expressed in terms of the band curvature or crystal harmonics44. The first- and second-order crystal harmonics of A1g symmetry and the first-order crystal harmonics of E2g symmetry and the position of the Fermi pockets of CsV3Sb5 are shown in Fig. 1d–f and illustrate the sensitivity of the experiment (The vertices derived from the crystal harmonics can be found in Supplementary Materials B. For details see ref. 45).

DFT simulations

DFT calculations were performed using VASP46 with plane wave augmented (PAW) pseudopotentials and a 300 eV energy cutoff. In all calculations, the pristine, SoD, and iSoD states were considered independently as 2 × 2 distortions. Lattice constants were calculated with pristine structures and kept fixed in CDW states. Minimum energy CDW states were found around 1.5% lattice distortion from the pristine structure. Structural and electronic calculations were performed on each of the three states. A 17 × 17 × 9 k-point grid was used for electronic calculations. The electronic response in the main text was approximated using the joint density of states with the following equation:

$${\chi }_{\mu \nu }^{{\prime\prime} }(\Omega)= \mathop{\sum}\limits_{k}{\gamma }_{{{{{{{{\bf{k}}}}}}}}}^{\mu }{\gamma }_{{{{{{{{\bf{k}}}}}}}}}^{\nu }{\int}\,d\omega {A}^{\mu }({{{{{{{\bf{k}}}}}}}},\omega ){A}^{\nu }({{{{{{{\bf{k}}}}}}}},\omega+\Omega )\\ \times [f(\omega )-f(\omega+\Omega )],$$
(2)

where

$${A}^{\mu }({{{{{{{\bf{k}}}}}}}},\omega )=\frac{1}{\pi }\frac{\Gamma }{{\Gamma }^{2}+{(\omega -{\epsilon }_{{{{{{{{\bf{k}}}}}}}}}^{\mu })}^{2}}.$$
(3)

In this equation, μ and ν are band indices, \({\gamma }_{{{{{{{{\bf{k}}}}}}}}}^{\mu }\) is the Raman vertex at momentum k and band μ, A(k, ω) is the spectral weight at momentum k and energy ω, Ω is the Raman shift energy, f(ω) is the Fermi-Dirac function, \({\epsilon }_{{{{{{{{\bf{k}}}}}}}}}^{\mu }\) is the band dispersion, Γ is the energy broadening. A broadening of 0.02 eV was used in the results in the main text. In the calculations, the Raman vertex \({\gamma }_{{{{{{{{\bf{k}}}}}}}}}^{\mu }\) is fixed at a value of 1. Thus, selection rules are ignored for the time being.

Phonon calculations were performed using the Phonopy code package47,48. A 3 × 3 × 4 k-mesh was utilized for the calculations. Our primary focus here is on the energy of the A1g phonon. In the pristine state, we observed a good agreement between the calculated phonons and those observed experimentally. Based on the success in previous studies49, for calculations comparing the pristine and CDW states, we employed DFT-3 to stabilize the phonon frequencies in the distorted phases, resulting in an overall frequency shift towards higher energy while maintaining reliable relative positions. Electron–phonon coupling to the A1g and E2g modes was calculated using the frozen phonon method and found to be negligible.

Reporting summary

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