Photoinduced metastable dd-exciton-driven metal-insulator transitions in quasi-one-dimensional transition metal oxides

Photoinduced phase transitions in matters have gained tremendous attention over the past few years. However, their ultrashort lifetime makes their study and possible control very challenging. Here, we report on highly anisotropic d-d excitonic excitations yielding photoinduced metal-insulator transitions (MITs) in quasi-one-dimensional metals Sr1-yNbOx using Mueller-Matrix spectroscopic ellipsometry, transient ultraviolet Raman spectroscopy, transient mid-infrared reflectivity and angular-resolved photoemission spectroscopy supported with density functional theory. Interestingly, the MITs are driven by photo-pumping of d-d excitons, causing the metallic a-axis to become insulating while the insulating b- and c-axis concomitantly become a correlated metal. We assign these effects to an interplay between the melting of charge and lattice orderings along the different anisotropic optical axes and Bose-Einstein-like condensation of the photoinduced excitons. The long lifetime in the order of several seconds of the metastable MITs gives greater flexibility to study and manipulate the transient excitonic state for potential applications in exciton-based optoelectronic devices. Due to recent developments in steady-state and ultrafast spectroscopic techniques there are more readily available methods to excite and observe anisotropic low-dimensional materials in transient states using light-matter interactions. Here, the authors observe photoinduced metal-insulator transitions in a quasi-one-dimensional metal, and analyse the role of d-d excitonic excitations in the transient state.

U sing light to manipulate fundamental physical properties of matter has gained tremendous attention in optical and condensed matter physics research. It has been shown that photoexcitation can induce transient exotic phases of matter that are not found in their equilibrium ground states. Examples, among others, include transient changes in crystal structures 1,2 , ferroelectricity 1 , metal-insulator transitions [2][3][4] (MITs), melting of spin and charge orders [5][6][7] , and even superconductivity 8,9 . The most fundamental way in which light can interact with matter is by exciting electrons from occupied to unoccupied states, creating electron-hole pairs that can bind to form excitons. Thus, excitons are expected to play important roles in the dynamics of these transient phases of matter. Since excitons are bosons, high-density excitons created by high-intensity photoexcitation can potentially condense into transient Bose-Einstein condensates [10][11][12], similar to what has been demonstrated by photoinduced magnon BEC transition driven by high-intensity microwave pumping 13 . However, the main difficulty with excitons (and other transient states of matter in general) is their ultrashort lifetime, which is often in the pico-to femtosecond range. This short timescale renders it challenging to probe and control these transient states.
Here, using a combination of Mueller-matrix spectroscopic ellipsometry, steady-state and transient ultraviolet Raman spectroscopies, transient mid-infrared reflectance, and angularresolved photoemission spectroscopy (ARPES) supported by theoretical calculations, we probe both the steady-state and dynamic dielectric responses of strongly anisotropic quasi-onedimensional (quasi-1D) correlated metals Sr 1−y NbO x of the type A n B n O 3n+2 as a model system. We reveal that the photoinduced pumping of low-energy d-d excitons in Sr 1−y NbO x dramatically changes their electronic, lattice, and optical properties. The d-d exciton pumping is found to drive complementary MITs along different optical axes, where the metallic axis switches to become insulating while the insulating axis concomitantly becomes more metallic by rearranging their charge and lattice orderings. The excited state is metastable with an extremely long lifetime of several seconds, caused by the slow recovery of the changes in lattice orderings and possible emergence of BEC-like excitonic phase. This long lifetime gives greater flexibility in manipulating the pumped state for both fundamental research and practical applications.

Results
Anisotropic properties of Sr 1−y NbO x . Sr 1−y NbO x is known to exhibit a rich phase diagram that strongly depends on the oxygen content 14 , ranging from isotropic metal SrNbO 3 (ref. 15 ), to a quasi-1D metal SrNbO 3.4 (refs. [16][17][18][19][20], and to ferroelectric insulator SrNbO 3.5 (ref. 21 ). Especially, the quasi-1D metal-like phases of Sr 1−y NbO x are ideal to study low-dimensional and MIT physics, as shown by their transition into an insulating charge density wave state at low temperatures [17][18][19] . The crystal structures of Sr 1−y NbO x are of the type Sr n Nb n O 3n+2 = SrNbO x , which represents a homologous layered perovskite-related series where the structure type, n, depends on the oxygen content, x. Along the c-axis, networks of NbO 6 octahedra are periodically grouped into n-octahedra thick slabs, while along the a-and b-axis the Nb-O-Nb bonds are chain-like and zig-zag-like, respectively 14 . For example, along the c-axis the slabs are 5-octahedra thick in n = 5 type SrNbO 3.4 (Fig. 1a, b), alternatingly 4-and 5-octahedra thick in n = 4.5 type SrNbO 3.45 , and unlimited in isotropic perovskite n = ∞ type SrNbO 3 . The chain-like bonds facilitate the metallicity along the a-axis, while the zig-zag-like bonds and slab structures hinder the charge hoppings between Nb ions along the b-and c-axis, respectively, making them more insulating. This arrangement makes Sr 1−y NbO x highly biaxially anisotropic, yielding an anisotropic dielectric tensor with different components of the complex dielectric function ε along different orthogonal optical axes. Thus, before probing their transient dynamical response, their steady-state diagonalized anisotropic dielectric tensors need to be determined using Mueller-matrix spectroscopic ellipsometry [22][23][24] .
Mueller-matrix spectroscopic ellipsometry. Representative samples of Sr 0.95 NbO 3.37 (an under-stoichiometric Sr-and O-deficient variant of n = 5 type SrNbO 3.4 ) and n = 4.5 type SrNbO 3.45 single crystals 14 are measured using Mueller-matrix spectroscopic ellipsometry within the photon energy range of 0.38-6.10 eV at room temperature. The resulting real parts of principal ε of the samples, Re[ε], are shown in Fig. 1c-e. Along the a-axis, the Re[ε a ] spectra of both Sr 0.95 NbO 3.37 and SrNbO 3.45 cross zero and become negative below 1.06 and 0.76 eV, respectively. In contrast, the Re[ε] of both samples along the b-and c-axes remain positive at all measured photon energies. This means both samples are metallic along the a-axis, but non-metallic along the b-and c-axes, indicating an intrinsic room-temperature quasi-1D metallic behavior consistent with previous electrical transport, ARPES, and infrared reflectivity results [17][18][19] . Figure 2a-c shows the imaginary parts of principal ε, Im[ε], of the samples, which are proportional to absorption spectra. These spectra also denote the quasi-1D metallicity of the samples, as shown by the presence of metallic Drude tail along the a-axis but not along the b-and c-axes. The Drude response contribution and the Re[ε a ] zero-crossing energy of Sr 0.95 NbO 3.37 are higher than those of SrNbO 3.45 , indicating a larger carrier density in Sr 0.95 NbO 3.37 than in SrNbO 3.45 consistent with their nominal electronic structures 14 (Nb-4d 0.16 for Sr 0.95 NbO 3.37 and Nb-4d 0.10 for SrNbO 3.45 ).
In the Im[ε b ] and Im[ε c ] spectra (Fig. 2b, c) at low energies, three strong peaks are observed at~0.7 and~1.2 eV along the baxis as well as at~1.1 eV along the c-axis (Table 1). Interestingly, the intensities of these peaks are higher in Sr 0.95 NbO 3.37 than in SrNbO 3.45 , similar to the trends of the a-axis Drude response caused by the difference in the carrier density between the two samples. This reveals that the three peaks originate from the excitations of electrons, which are anisotropically-localized along the b-and c-axes but mobile along the a-axis. As discussed below (Fig. 3a), this is indeed the case; more precisely, the three peaks originate from d-d transitions between split Nb-4d bands across the Fermi level along the b-and c-axes. Thus, we name these three peaks as the d-d excitations.
At higher energies, a distinct absorption edge is seen in the Im[ε] spectra along the a-and b-axes at~4.4 eV for Sr 0.95 NbO 3.37 and~4.2 eV for SrNbO 3.45 due to the O-2p→Nb-4d chargetransfer inter-band transitions (see "Discussion" below). Meanwhile, in the intervening energy range of 2-4 eV the Im[ε a ] and Im[ε b ] of both samples are very close to zero, signifying the visible-range transparency of both samples along the a-and baxes. In contrast, the Im[ε c ] spectra of both samples are quite absorbing above the d-d excitations, characterized by the presence of several wide "humps" at varying energy positions (Table 1). Between the two samples, the overall intensities of these humps remain relatively the same (unlike the d-d excitations), indicating that these humps do not originate from carrier excitations. Instead, based on the crystal structure in Fig. 1a, b, these humps could be caused by the presence of extra O layers every few unit cells along the c-axis that create new occupied and unoccupied states that contribute to the optical absorption and modulate the shapes of ε c .
Excitonic ultraviolet Raman spectroscopy. To further probe these d-d excitations, we perform excitonic ultraviolet Raman spectroscopy ( Fig. 2b inset) on the n = 5 type Sr 0.95 NbO 3.37 sample with an incoming beam of 240 nm (5.17 eV), i.e., on the onset of the O-2p→Nb-4d charge-transfer inter-band transitions. Along the b-axis, we find an excitonic peak centered at 0.89 eV Raman shift consistent with the lower d-d excitation, indicating the excitonic nature of these d-d excitations. Interestingly, a similar excitonic peak is also found at 0.86 eV along the a-axis, which means that the lower d-d exciton also occurs along the metallic axis. In conventional metals, excitons are usually absent. Despite this, excitons are present in Sr 1−y NbO x because they are not conventional metals but rather correlated quasi-1D metals. In the Im[ε a ] obtained from Mueller-matrix ellipsometry, the a-axis d-d exciton is overshadowed by the Drude response of the correlated electrons in the metallic direction (see Fig. 2a), and the use of Raman spectroscopy allows us to resolve the exciton since Drude excitations are usually invisible in optical Raman.
Electronic band structure. To determine the origins of the peaks in Im[ε] spectra, we calculate the electronic band structure of n = 5 type SrNbO 3.4 (which is closely related to n = 5 type Sr 0.95 NbO 3.37 and n = 4.5 type SrNbO 3.45 ) using density functional theory in Fig. 3a. The results are consistent with both experimental ARPES and ultraviolet photoemission (UPS) results and previous theoretical calculations 17,19,20 . The band structure is plotted along the high symmetry lines of Γ-X (along the a-axis), Γ-Y (b-axis), and Γ-Z (c-axis) to determine the possible valence and conduction band pairings that contribute to the Im[ε] spectra along each axis. The results show that the valence bands have mainly O-2p character while the conduction bands have mainly Nb-4d character, and together they contribute to the O-2p→Nb-4d charge-transfer inter-band transition edges.
Although the Nb-4d bands are mostly unoccupied and lie above the Fermi level, a small group of Nb-4d bands (red bands in Fig. 3a) cross the Fermi level, E F , along Γ-X and lie occupied below it at Γ, along Γ-Y, and along Γ-Z. The strong dispersion and E F crossing along Γ-X are consistent with the samples' metallic behavior along the a-axis and responsible for the Drude response excitation. Meanwhile, at Γ, along Γ-Y, and along Γ-Z, these bands lie below the E F with no significant dispersion, consistent with the samples' non-metallic behavior along the band c-axes. The low-energy excitonic peaks in Im[ε] spectra can then be assigned to the transitions (green arrows in Fig. 3a) from these shallow occupied bands to the low-lying unoccupied bands at Γ, along Γ-Y, and along Γ-Z (blue bands in Fig. 3a). As both occupied and unoccupied bands have Nb-4d character, these lowenergy peaks are d-d excitations. Although d-d transitions are dipole forbidden in centrosymmetric compounds, they are distinctly observed here due to the symmetry breaking caused by the layered perovskite structure. Thus, the Drude response and the d-d excitons originate from the same group of Nb-4d bands, but along different directions in the reciprocal Brillouin zone and thus the real space.
Furthermore, we also perform room-temperature ARPES on the Sr 0.95 NbO 3.37 sample to verify the band structure calculations.  Figure 3b shows the band dispersion of the low-lying occupied Nb-4d bands along the X-Г-X direction. We see two dispersing bands along Г-X direction crossing the Fermi level indicative of its metallic behavior. We observe two arms of the parabolic band (as obtained from the first-principles calculations, see Fig. 3a), while the ARPES intensity at the Г point is not visible. This discrepancy could be due to the photoelectric matrix element for the chosen photon energy; however, it does not affect our main discussion. The iso-energy Fermi surface is shown in Fig. 3c. The Fermi surface is highly anisotropic; it is elongated along the Y-Г-Y direction while restricted along the X-Г-X direction. We see two parallel linear features, which are characteristic for their unidirectional electronic structure.  Fig. 4b shows that upon turning on the pump beam, R trans (a) drastically decreases all the way down to the steady-state reflectance of the non-metallic b-axis, R b , indicating a near-100% switching from metal to insulator. When the pump beam is turned off, R trans (a) recovers back to the steadystate metallic level, R a , indicating a relaxation toward the initial state. The relaxation times of the pump-on and pump-off conditions are found to be in the order of several seconds; in this particular orientation, they are fitted to be 5.8 ± 0.2 s and 4.6 ± 0.2 s, respectively.
As the optical response of the a-axis within the MIR range is dominated by the metallic Drude response 18,19 , a decrease in its MIR transient reflectance indicates a decrease of the Drude peak, which directly translates to a decrease in the carrier density 23 . Thus, the drastic, nearly 100% decrease of R trans (a) toward the steady-state insulating level in Fig. 4b is strongly suggesting an exciton-driven transient metal-insulator transition (MIT), indicating a photoinduced switching capability of Sr 1−y NbO x .
To prevent excessive heat damage, in Fig. 4c n = 5 type Sr 0.95 NbO 3.37 is pumped with a lower power density of 260 Wcm −2 , which results in lower decrease of R trans (a) but excellent repeatability of the switching. Intriguingly, when E probe is parallel to the b-axis, the 1.2 eV d-d exciton pumping causes an increase of the transient reflectance (and thus the metallicity) along the b-axis, R trans (b). This means that while the exciton pumping is switching the metallic a-axis to be more insulating, it also concomitantly switches the insulating b-axis to be more metallic (i.e., insulator-metal transition or IMT), making the strongly anisotropic Sr 0.95 NbO 3.37 effectively more isotropic. More evidence can be seen in the power density, P pump , dependence of the switching in Fig. 4d, which shows that while R trans (a) decreases linearly with increasing P pump , R trans (b) increases concomitantly instead, outlining charge conservation. The switching effect can also be observed when E pump // a-axis due to the presence of the~0.9 eV d-d exciton along the a-axis as and SrNbO 3.45 , respectively. Inset is excitonic ultraviolet (UV) Raman spectra of the samples along the aand b-axes. These spectra, normalized with respect to the d-d transition peaks along the b-axis, are also superimposed on the main panels to directly compare them with the Im[ε] spectra. For reference, the UV Raman spectrum of Si is also shown. The energy position of each peak is determined from their respective apparent maxima, except for O-2p→Nb-4d peaks where it is determined from their respective linearly extrapolated edge instead.
revealed by ultraviolet Raman spectroscopy (Fig. 2d), showing further evidence of the exciton-driven nature of the switching.
Transient pump-probe phononic ultraviolet Raman spectroscopy. Furthermore, to study the effect of the exciton pumping on the transient lattice and charge orderings, we perform transient   26 ), and spin-ladder compounds 27 . Meanwhile, along the a-axis (Fig. 5b), only the 830 cm −1 mode can be distinctly observed, while the rest are suppressed. According to Fig. 1a, b, the Nb-O-Nb bonds along the metallic a-axis are chain-like, while along the insulating b-axis they are zig-zag-like. Thus, as the 440, 560, and 680 cm −1 modes are observed only along the b-axis but not along the a-axis, these modes are signatures of the zig-zag-like bonds but not the chain-like bonds. When the exciton pumping is turned on, all these zig-zag-likerelated phonon modes decrease dramatically with increasing P pump , indicating that the pumping changes the lattice orderings of the Nb-O-Nb bonds particularly along the b-axis. These decreases can already be observed even at the lowest P pump of 300 Wcm −2 . At the highest P pump of 5.7 kWcm −2 , the zig-zag-likerelated modes become either severely diminished or completely bleached, and the shape of the Raman spectrum along the b-axis approaches that of along the a-axis. This indicates that the zig-zag-like Nb-O-Nb bonds along the b-axis are transformed by the d-d exciton pumping into more chain-like bonds, which facilitates easier hoppings between Nb ions and increases the conductivity of the normally insulating b-axis, making the a-and b-axes more isotropic consistent with pump-probe MIR-reflectance results. Note that other effects, such as screening of phonon modes by the excited photoelectrons and thermal heating by the laser pump, are unlikely to play significant roles in the evolution of the transient Raman spectra, as discussed in more detail in "Methods" and Supplementary Discussion.

Discussion
As mentioned, transient states caused by electronic and/or excitonic excitations typically have ultrashort lifetime in the pico-to femtoseconds range. Thus, the seconds-long ultraslow recovery time of the transient MITs in Fig. 4 indicates that the typically ultrafast excitonic excitations couple to additional mechanisms that have very slow recovery time. We believe that there are mainly two mechanisms that are responsible for this ultraslow recovery time.
First, as discussed above, the d-d exciton pumping causes the zig-zag-like Nb-O-Nb ordering along the b-axis to transform into more chain-like bonds. As this transient IMT involves changes in the lattice structure, this is an important reason for the slow recovery time along the b-axis, as recovery of lattice structure changes is typically orders of magnitude slower than recovery of electronic transitions.
For the long-lasting transient MIT along the a-axis, we are proposing a mechanism, in which the d-d exciton photopumping causes the conversion of most of the free electrons into excitons, depleting the red Nb-4d band in Fig. 3a, causing the decrease of the a-axis metallicity, and creating a large density of excitons. Due to the much lower effective mass of excitons (compared to atomic mass), this large density of excitons can undergo Bose-Einstein-like condensation (BEC) even at room temperature [10][11][12]28,29 , similar to what has been observed in the case of photo-pumped magnons in yttrium-iron-garnet films 13 . The coherence of the BEC phase can lead to a very long lifetime of the transient insulating state. For example, in photopumped magnons 13 , non-BEC phase decays quickly within 100-200 ns while the BEC phase stays coherent even after 1200 ns.
Note that these two mechanisms (changes in the lattice orderings and BEC-like phase transition) may very well be coupled, as together they resemble the signatures of excitonic insulators, a manifestation of exciton BEC in which the insulating ground state is dominated by BEC of excitons accompanied by changes in the lattice orderings 28,29 . Similar behaviors have been predicted and suspected to be observed in the two likely candidates for intrinsic excitonic insulators: semiconducting Ta 2 NiSe 5 (ref. 30 ) and semimetal 1T-TiSe 2 (ref. 31 ).
Furthermore, with high enough pump power density of 600 Wcm −2 , the switching can be made to be nearly 100%, promising potential applications in future photoinduced switching devices such as exciton-based transistors and other optoelectronic devices in general. This is especially important because so far, many other photoinduced systems have only been able to be optically switched by <35% (refs. [32][33][34][35], and/or need high switching power density requirements of >10 5 -10 10 Wcm −2 (refs. [32][33][34][35][36][37]. Thus, the near-100% optical switching of Sr 1−y NbO x , which only needs a very low pump power density of 600 Wcm −2 to induce the switching, represents a very big leap compared to other photoinduced systems, conceptually demonstrating that it is possible to optically switch a system to near-100% switching contrast with very low pump power density.

Methods
Sample preparation. Melt-grown crystalline n = 4.5 type SrNbO 3.45 and Sr-and O-deficient n = 5 type Sr 0.95 NbO 3.37 samples are prepared by melting, reducing, and solidifying the corresponding fully oxidized Nb 5+ compositions of SrNbO 3.50 and Sr 0.95 NbO 3.45 under a flow of 98% Ar + 2% H 2 gas 14 . The process is done in a GERO mirror furnace where two polycrystalline sintered rods with fully oxidized Nb 5+ compositions of SrNbO 3.50 and Sr 0.95 NbO 3.45 , respectively, are processed by floating zone melting. The two polycrystalline sintered rods themselves are prepared by mingling an appropriate molar ratio of SrCO 3 and Nb 2 O 5 , which is then pre-reacted at an elevated temperature in air. After the pre-reaction, the mixture is ground into powder, once again mingled, pressed into the shape of two rectangular rods, and sintered at an elevated temperature in air. The experimental approaches, types, and design of used equipment, devices, and constructions are similar to those which are presented comprehensively in ref. 38 . The GERO mirror furnace is presented in Appendix 1 of ref. 38 . Photo images of melt-grown crystalline pieces of n = 4.5 type SrNbO 3.45 and non-stoichiometric n = 5 type Sr 0.95 NbO 3.37 are shown in Supplementary Fig. 1. Pieces of the crystalline samples are then cleaved into flat plate shapes so that their surfaces are parallel to the c-axis (verified with X-ray diffraction, see below). A transmission electron microscopy (TEM) image of n = 4.5 type SrNbO 3.45 is shown in ref. 14 .
X-ray diffraction. The cleaved plate-shaped n = 5 type Sr 0.95 NbO 3.37 and n = 4.5 type SrNbO 3.45 samples are measured using high-resolution X-ray diffraction to characterize their lattice structures and verify the orientation of their cleaved surfaces. The measurements are done using a Huber 4-circle diffractometer system 90000-0216/0 at Singapore Synchrotron Light Source with a selected X-ray wavelength equal to that of Cu Kα 1 radiation (λ = 1.5406 Å). The resulting 2θ/θ XRD patterns of both samples are shown in Supplementary Fig. 2. Each major peak in both patterns is a higher-order mode of the (001) Bragg peak, which means that the surface normal of both samples are parallel to the c-axis. Further analysis results in a c-axis lattice constant of 32.404 and 59.300 Å for Sr 0.95 NbO 3.37 and SrNbO 3.45 , respectively, consistent with previous results 14,16 .
Mueller-matrix spectroscopic ellipsometry. As the Sr 1−y NbO x samples are highly anisotropic quasi-1D metals, an advanced form of ellipsometry called Mueller-matrix spectroscopic ellipsometry is needed to unambiguously probe their principal dielectric functions along all optical axes [22][23][24] . Mueller matrix is a 4 × 4 matrix unique to each material that describes the changes in light polarizations due to the complex dielectric response of said material 23 . Conventional optical absorption spectroscopy techniques typically only measure a few elements of this matrix, making them suitable only for probing isotropic materials. In contrast, Mueller-matrix spectroscopic ellipsometry measures the majority of these elements (in some cases all), enabling us to precisely probe the principal dielectric tensors of highly anisotropic materials along all orthogonal directions. More information and a basic introduction about Mueller-matrix spectroscopic ellipsometry are given in Supplementary Methods.
In this study, the Mueller-matrix spectroscopic ellipsometry measurements are done from 0.38 to 6.10 eV using a Woollam V-VASE ellipsometer with a compensator and rotating analyzer. The cleaved samples are mounted on a precision rotation stage (Newport RS40) to perform azimuth-dependent measurements, where the in-plane rotation angle, φ, is varied from 0°to 315°in steps of 45°. At each in-plane orientation, the measurements of each Muellermatrix element, m ij , are done at three incident angles, θ, of 50°, 60, and 70°from the sample surface normal. Such an angle-resolved measurement scheme is necessary to ensure a complete characterization of arbitrary optically anisotropic samples [22][23][24] . This setup is capable of measuring 12 out of the 16 Mueller-matrix elements (from m 11 to m 34 ), which is sufficient to obtain the principal ε of highly anisotropic samples.
The resulting incident-angle-, azimuth-dependent Mueller-matrix element spectra are analyzed using the Woollam WVASE software. The fitting parameters are the principal ε of the samples along the major optical axes and the Euler angles of α, β, and γ. The principal dielectric functions, ε a , ε b , and ε c along the a-, b-, and c-axis, respectively, are modeled using the Kramers-Kronig transformable Drude 23 and Herzinger-Johs PSemi-Tri 39 oscillator functions. Meanwhile, real-valued and wavelength-independent Euler angles describe the rotation between the Cartesian laboratory frame of (x, y, z) and the samples' Cartesian optical axis frame of (a, b, c): α represents a rotation around the z-axis to rotate from (x, y, z) to (x′, y′, z), β represents a rotation around the x′-axis to rotate from (x′, y′, z) to (x′, y″, z′), and γ represents a rotation around the z′-axis to rotate from (x′, y″, z′) to (a, b, c). The samples' surface roughnesses (~8 nm for n = 5 type Sr 0.95 NbO 3.37 and~5 nm for n = 4.5 type SrNbO 3.45 ) are modeled by a Bruggeman-mode effective medium approximation 23 with 50% material and 50% void (ε void = 1 + i0).
The analysis is done using non-linear regression methods, where measured and calculated Mueller-matrix elements are matched until the mean-squared error (MSE) between the fit and the data is minimized. Each sample is analyzed in a multi-sample configuration analysis scheme 24 , where data from all in-plane orientations and incident angles are included in the regression analysis and only the azimuthal Euler angle of α is set according to the in-plane rotation measurement configuration (φ n+1 = φ n + 45°, thus α is also set such that α n+1 = α n + 45°). The Mueller-matrix spectroscopic ellipsometry spectra are measured in an extended energy setup: the extended infrared part from 0.38 to 1.00 eV and the infrared-visible-ultraviolet part from 0.60 to 6.10 eV, both in steps of 0.02 eV. In the regression analysis, these two parts are fit simultaneously to obtain the complete principal ε from 0.38 to 6.10 eV. As representative examples, the comparisons between measured and fitted Mueller-matrix elements after the final fit for φ = 0°, 45°, 90°, and 135°; θ = 70°; and energy range of 0.6-6.1 eV are shown in Supplementary Fig. 3 (for Sr 0.95 NbO 3.37 ) and Supplementary Fig. 4 (for SrNbO 3.45 ).
The resulting principal ε of Sr 0.95 NbO 3.37 and SrNbO 3.45 are shown in Figs. 1 and 2. The analysis also reveals that the Euler angle of β of both samples is very small (<0.1°for Sr 0.95 NbO 3.37 and 0.6°for SrNbO 3.45 ), indicating that the optical caxis of the samples coincides with their respective surface normal and thus, per XRD results ( Supplementary Fig. 2), with their respective crystallographic c-axis. These minute β also mean that the Euler angles of α and γ are practically equivalent (since the z-axis is almost unchanged by the rotation of β), and the combined angle of α + γ can be used to determine the orientation of the a-and b-axis with respect to the plane of incident (POI) at a given φ. For Sr 0.95 NbO 3.37 at φ = 0°, the a-axis (b-axis) is oriented at −11.8°(78.2°) from the intersection line between the POI and the sample surface. Meanwhile, for SrNbO 3.45 at φ = 0°, the a-axis (b-axis) is oriented at −8.4°(81.6°) from the intersection line between the POI and the sample surface.
Excitonic ultraviolet Raman spectroscopy. Ultraviolet Raman spectroscopy measurements of excitons are performed with the UT-3 Raman spectrometer 40 with 1800 s integration time. The 240 nm probe beam is obtained by frequency tripling of a Tsunami Ti:Sapphire laser (model 3950-X1BB, Spectra Physics Lasers Inc., repetition rate: 80 MHz) with a spot size of 15 µm and a power of 5.8 mW. The spectral response of the spectrometer is calibrated using a certified white light calibration lamp from Gigahertz Optik (DKD).
Density functional theory calculations. Density functional theory (DFT) calculations are done using the Perdew-Burke-Ernzerhof 41 (PBE96) exchangecorrelation potential and the projector-augment wave (PAW) method 42 as implemented in the Vienna ab initio simulation package 43 (VASP). In these calculations, Sr-4s4p5s, Nb-4p5s4d, and O-2s2p orbitals are treated as valence states, employing the PAW potentials labeled as "Sr_sv", "Nb_sv", and "O" in the VASP PBE library. The cutoff energy for the plane-wave basis set is set to 500 eV and the partial occupancies for each orbital use the Gaussian smearing with a width of 0.2 eV. The atomic structure of n = 5 type SrNbO 3.4 is taken from experimentally determined atomic positions in ref. 16 which is modeled by supercells containing 54 atoms with a space group of Pnnm. The band structure is calculated with 23 × 17 × 3 Γ-centered Monkhorst-Pack k-point meshes. The Fermi level is adjusted so that it is consistent with previous electrical transport, ARPES, and infrared reflectivity results [17][18][19] . The calculated band structure of SrNbO 3.4 near the Fermi level is presented in Fig. 3a, while the extended version down to E-E F = −7.5 eV is shown in Supplementary Fig. 5a. Note that in the extended version, the deep-lying O-2p band is located below E-E F = −3 eV, rather than −4 eV, according to the UPS results 17 , due to the well-known Kohn-Sham bandgap underestimation problem in DFT. Similar DFT calculation results of SrNbO 3.4 that showed the O-2p bands have also been reported previously in ref. 17 .
Angular-resolved photoemission spectroscopy (ARPES). The ARPES measurements were performed at the SUV beamline 44 of Singapore Synchrotron Light Source (SSLS) using a Scienta-Omicron DA30L electron analyzer. The single crystalline sample of Sr 0.95 NbO 3.37 is cleaved inside the load lock chamber under pressure 5 × 10 −8 mbar using the standard top-post method. The sample is then immediately transferred to the analysis chamber with base pressure 1 × 10 −10 mbar. The measurements were performed at room temperature using helium lamp source (photon energy = 21.21 eV). An ARPES cut of the n = 5 type Sr 0.95 NbO 3.37 sample along the a-(Γ-X) and b-axis (Γ-Y) is presented in Fig. 3b and Supplementary Fig. 5b, respectively. The ARPES cut along the a-axis (b-axis) is taken at k y = 0 (k x = 0) to ensure that there is no momentum contribution along the b-axis (a-axis). The ARPES cut along the Γ-Y direction shows a weak and non-dispersive band between E B = −(E-E F ) = 0.2 eV and 0.6 eV, consistent with the DFT calculation in Fig. 3a that also shows non-dispersive bands at around E-E F = −0.5 eV along the Γ-Y direction. Meanwhile, the Fermi surface map (Fig. 3c) is obtained using the electrostatic deflection lensing functionality of a DA30L analyzer without rotating the sample.
Mid-infrared transient pump-probe reflectivity. Since Mueller-matrix spectroscopic ellipsometry shows an onset of the Drude response for energies of the order of~1 eV in the metallic direction, the reflectance of a laser-based mid-infrared (MIR) beam with a wavelength of 7 μm (~0.18 eV) probes predominantly the free electronic carriers associated to the Drude response. The main source laser for the MIR-reflectance setup (c.f., Fig. 4a) is a fiber amplified laser (Tangerine HP, 35 W) supplying typically 300 femtosecond pulses with 70 μJ at a 50 kHz repetition rate into the difference frequency generation setup as described by the following stages. The 1st stage is a supercontinuum generation in a YAG-crystal and second harmonic generation in a beta barium borate (BBO) type 1 crystal with 1030 nm pump. The 2nd stage is an optical parametric amplification of 515 nm pump and supercontinuum seed in BBO type 2 crystal to generate a near-infrared beam of 1100-1300 nm. The 3rd stage is a differential frequency generation of 1030 nm pump and near-infrared seed in an AGS-crystal to generate a MIR beam of 6-12 µm. The MIR beam is focused on the sample using an on-axis parabolic mirror. The pump beam is focused on the sample through a hole in the same parabolic mirror. The reflected intensity is recorded using a thermopile power sensor (Coherent PS10). Spot diameter sizes of~0.3 mm are determined by knifeedge experiments of pump and probe beams. The wavelength of the probe is measured with an integrated FTIR-spectrometer utilizing a pyroelectric sensor. Pump-on and pump-off are switched by an optical shutter. Data shown in Fig. 4b, c are real-time measurements of the observed reflected intensity.
The pump-on relaxation time constant, τ on , is fitted from the red solid curve in Fig. 4b using where t 0 is the turn-on time point, y 0 is the background level to which R trans approaches as time, t, goes to infinity if the pump is perpetually turned on, and A is the amplitude of the R trans change. Meanwhile, the pump-off relaxation time constant, τ off , is fitted from the blue solid curve in Fig. 4b using For both fittings, y 0 and A are identical within the error bars. From this analysis, τ on and τ off is estimated to be 5.8 ± 0.2 s and 4.6 ± 0.2 s, respectively.
Transient pump-probe Raman spectroscopy. Raman spectroscopy measurements are performed using the UT-3 Raman Spectrometer 40 with 300 s integration time. The 260 nm probe beam is obtained by frequency tripling of a Tsunami Ti:Sapphire laser (model 3950-X1BB, Spectra Physics Lasers Inc., repetition rate: 80 MHz) with a spot size of 15 µm and a power of 2.8 mW. The 1030 nm pump beam is provided by a Tangerine fiber laser (Amplitude Systemes, repetition rate: 500 kHz) with a spot size of 50 µm. The power of the pump beam is varied between 10 and 70 mW with a polarizer λ/2-waveplate combination, also controlling the polarization of the pump beam. The polarization of the probe beam is fixed, and the relative polarization with respect to the sample axes is varied by rotating the sample. Spatial overlap is ensured by imaging the laser focus on the sample. Since transient reflectivity measurements show timescales longer than the repetition rate of the laser systems, there is no need for temporal overlap of the laser pulses.
The effects of thermal heating from the pump laser are estimated by studying the changes in width and frequency of the phonon modes as a function of pump power density. This is because according to the anharmonic decay model 45 , the linewidth of phonons is dependent on the temperature and thereby a good indicator for heating effects (Supplementary Fig. 6). From this we derive that the heating effect for pump power densities of up to 300 Wcm −2 is equivalent to an increase in temperature of <50 K, since there is no significant change in the linewidth for this power density. Heating only becomes significant (in terms of increasing the sample temperature) for pump power densities above 1 kWcm −2 , which are used only for pump-probe Raman but not for pump-probe MIR reflectance.

Data availability
The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability
The theoretical band structure is calculated using the openly-available VASP program and the implementation codes are available from the corresponding authors upon reasonable request.