Unveiling the orbital-selective electronic band reconstruction through the structural phase transition in TaTe$_2$

Tantalum ditelluride TaTe$_2$ belongs to the family of layered transition metal dichalcogenides but exhibits a unique structural phase transition at around 170 K that accompanies the rearrangement of the Ta atomic network from a"ribbon chain"to a"butterfly-like"pattern. While multiple mechanisms including Fermi surface nesting and chemical bonding instabilities have been intensively discussed, the origin of this transition remains elusive. Here we investigate the electronic structure of single-crystalline TaTe$_2$ with a particular focus on its modifications through the phase transition, by employing core-level and angle-resolved photoemission spectroscopy combined with first-principles calculations. Temperature-dependent core-level spectroscopy demonstrates a splitting of the Ta $4f$ core-level spectra through the phase transition indicative of the Ta-dominated electronic state reconstruction. Low-energy electronic state measurements further reveal an unusual kink-like band reconstruction occurring at the Brillouin zone boundary, which cannot be explained by Fermi surface nesting or band folding effects. On the basis of the orbital-projected band calculations, this band reconstruction is mainly attributed to the modifications of specific Ta $5d$ states, namely the $d_{XY}$ orbitals (the ones elongating along the ribbon chains) at the center Ta sites of the ribbon chains. The present results highlight the strong orbital-dependent electronic state reconstruction through the phase transition in this system and provide fundamental insights towards understanding complex electron-lattice-bond coupled phenomena.

One prime example is the charge density wave (CDW) order, which is described as a long-range periodic modulation of the electronic distribution with a concomitant lattice distortion [3][4][5].Many types of CDW phases have been established in TMDCs (e.g., TaS2 and NbSe2) with their associated electronic properties such as metal-insulator transition and superconductivity [6,7].On the other hand, the superperiodic lattice ordering (or superstructure) had also been considered from the viewpoint of molecule-like bonding of relevant orbitals [8].Particularly in tellurides MTe2, the importance of M-Te charge transfer and Te-Te overlap has been argued, which may make the picture of M-M and/or Te-Te local bonding more plausible as compared to sulfides and selenides [9][10][11][12].Indeed, the CdI2-type MTe2 [see Figs.1(a) and 1(d) for the undistorted trigonal 1T case] hosts various superperiodic patterns/clusters indicative of molecule-like bonding, such as Mo/W zigzag chains in (Mo,W)Te2 [13], Ir dimers in IrTe2 [14], and Te dimers in AuTe2 [15].Among them, group-V MTe2 (M = V, Nb, Ta) is a common system that crystallizes in a monoclinic (3×1×3) superstructure at room temperature [Fig.1(b); hereafter referred to as 1T"] [16,17].This metallic 1T" state is characterized by the quasi-onedimensional M double zigzag (ribbon) chains, that might also be viewed as the superposition of linear M trimers in two directions (black dashed lines in Fig. 1(b)) [8,9].Related to the large and anisotropic nature of lattice distortion, several unusual phenomena have been observed in VTe2, such as the vanishment of topological surface states through the 1T-1T" phase transition [18] and the photoinduced generation of transverse acoustic phonons [19,20].Thus, the clustered MTe2 compounds show a lot of promise for emerging novel electron-lattice-bond coupled phenomena.
We note that this LT structure is unique to TaTe2 and has not been observed in other TMDCs including its sister compounds such as TaX2 (X =S, Se) or MTe2 (M = V, Nb).At Ts, the electrical resistivity (magnetic susceptibility) shows an abrupt drop (increase) on cooling [21] whereas the Seebeck coefficient indicates a sign inversion [24], thereby suggesting the modifications of the electronic band structure.Recent investigations have shown that the 1T"-LT phase transition can be controlled by various approaches such as chemical substitution [24][25][26][27], pressure application [28], photodoping [29], reduced dimensionality [30,31], and some of them also induce superconductivity [25,26,28].
Nevertheless, the underlying mechanism of the 1T"-LT transition is still controversial, and multiple scenarios have been proposed in terms of Fermi surface nesting [27,32], anisotropic electron-phonon coupling [21,27], and local chemical bonding [24,[33][34][35][36]. Since comparable Ta 5d and Te 5p states are theoretically predicted to reside near the Fermi level [10,11,21,29,34], resolving the orbital-specific modifications in the electronic states through the 1T"-LT transition may provide important clues to fully discuss this complex phase transition and related physical properties.
In this Article, we investigate the electronic structure of single crystalline TaTe2 and its modifications through the 1T"-LT transition by utilizing core-level and angle-resolved photoemission spectroscopy (core-level PES and ARPES) with first-principles calculations.Our temperaturedependent measurements reveal a sizeable splitting of the Ta 4f core-level PES spectra and an unusual kink-like band reconstruction at the Brillouin zone boundary, demonstrating the significant orbitaldependent electronic state modifications in this system.

II. Methods
Single crystalline TaTe2 were grown by the chemical vapor transport method using iodine as a transport agent.Stoichiometric mixture of Ta and Te powders and iodine were sealed in evacuated quartz tubes and reacted for about one week in a three-zone furnace.The temperatures of the source and growth zones were set to 900 and 800 °C, respectively.Details regarding the sample characterizations, including the electrical resistivity, Seebeck coefficient, and low-energy electron diffraction measurements, are provided in Supplemental Material [37].
Core-level PES measurements were performed at BL28A in Photon Factory (KEK) using a system equipped with a Scienta Omicron SES2002/DA30 electron analyzer.The photon energy and energy resolution were set to 90 eV and 30 meV, respectively.High-resolution ARPES measurements were conducted at the Department of Applied Physics, The University of Tokyo, equipped with a VUV5000 He-discharge lamp and Scienta Omicron DA30 electron analyzer.The photon energy (hν) and energy resolution were set to 21.2 eV (HeIα) and 16 meV, respectively.For all measurements, the samples were cleaved in-situ at around room temperature to obtain a fresh (0 0 1) plane and the vacuum level was kept better than 2 × 10 -10 Torr throughout the measurements.The Fermi level of the samples was referenced from the Fermi-edge spectra of polycrystalline gold electrically in contact with the samples.For the ARPES data analysis, we used an empirically obtained work function of 4.9 eV.
The electronic band structures were calculated by using OpenMX code [38].For the virtual 1T phase, we adopted the local density approximation (LDA) with the Perdew-Zunger parametrization for the exchange-correlation functional in the density functional theory [39] and a 8 × 8 × 8 k-point mesh for the calculations of the self-consistent electron density and the structural optimization.We optimized the lattice structure of the virtual 1T phase by relaxing the primitive translational vectors and atomic positions in a non-relativistic calculation with the convergence criterion less than 0.01 eV/Å about the interatomic forces.The optimized lattice constants were at = 3.636 Å and ct = 6.674Å.
Using the optimized structures, we calculated the electronic band structures by a relativistic ab initio calculation, where the relativistic effects are included by a fully relativistic j-dependent pseudopotential.For the 1T" and LT phases, we calculated the electronic band structures by the generalized gradient approximation (GGA) using the experimentally reported structural parameters in the literature [21].We adopted the Perdew-Burke-Ernzerhof GGA functional in density functional theory [40], a 8 × 8 × 8 k-point mesh, and a fully relativistic j-dependent pseudopotential for the calculations of the self-consistent electron density.For direct comparison with ARPES data, we constructed the proper spectral weights by employing the unfolding procedure [41,42] based on the primitive (virtual) 1T unit cell.

III. Results
A. Core-level spectra.
First, we demonstrate the temperature dependence of the core-level PES spectra that provides direct insight into the atomic-site specific electronic modulations.Figure 2(a) presents the overall core-level spectra in the high-temperature 1T" phase (320 K) collected using a synchrotron light source (hν = 90 eV).The intense Ta 4f and Te 4d doublet peaks are discerned at binding energies (EB) of 22-25 and 39-42 eV, respectively, together with other core-levels (see the magnified profile depicted by orange).
Figures 2(b) and 2(c) show the temperature dependence of the Ta 4f7/2 core-level intensity demonstrated as the color map and the set of spectral profiles, respectively.They are collected in the temperature range from 320 to 20 K during the cooling process.The spectral profile of Ta 4f7/2 above Ts (~170 K) is broad and asymmetric with its peak position nearly fixed at EB ~ 22.7 eV.Upon lowering the temperature below Ts, the peak position gradually shifts toward lower EB and a multi-peak structure emerges.This temperature-dependent splitting is reproduced in the temperature-cycle and also by bulk-sensitive soft x-ray measurements [37], thereby substantiating its bulk origin.The fitting analysis using Voigt functions with a Sherly-type background yields the maximum splitting energies of 0.11 (3) eV and 0.31(3) eV for 1T" (320 K) and LT (20 K), respectively, as displayed by the black markers and dotted curves in Fig. 2(c) (see Supplemental Material [37] for more details).This implies that the variation of the electron densities among the inequivalent Ta sites (i.e., d-d charge transfer) is substantially enhanced across the transition.Meanwhile, we note that these splitting energies are much smaller as compared to those in the Star-of-David CDW systems such as 1T-TaS2 (~1.2 eV) [43] and 1T-TaSe2 (~0.9 eV) [44], where strong electron-electron correlation effect (Mott transition) often intertwines with the √13 × √13 superperiodic state [6,45,46].
Similarly, the temperature dependence of the Te 4d5/2 core-level is extracted as shown in Figs.

2(d) and 2(e)
. Since there are three inequivalent Te sites in 1T", the spectra above Ts already feature a multi-peak structure.In contrast to Ta 4f7/2, the Te 4d5/2 spectral distribution hardly changes even below Ts.This indicates that the charge redistribution among the Te sites (p-p charge transfer) across the transition is negligible compared to that of the Ta sites.On the other hand, we find a slight shift of the peak maximum toward a lower EB at lower temperatures as indicated by the orange circle markers in Fig. 2(d).This is more clearly seen in the overlaid profiles at 320 K (red) and 20 K (blue) in Figs.
2(e) and 2(f), where the peak positions differ by about 45 meV.To examine this shift more precisely, we compare the temperature dependence of the energy shift (relative to the value at 20 K) estimated by the position of the highest intensity peak for Te 4d5/2 (orange circles) and the center of the spectral weight for Ta 4f7/2 (purple triangles) and Te 5d (including both 4d5/2 and 4d3/2, cyan rectangles), as displayed in Fig. 2(g).Remarkably, both the Ta 4f and Te 5d shifts show nearly the same temperature dependence, indicating that the amount of the Ta-Te charge transfer (d-p charge transfer) is not significantly modified upon the 1T"-LT transition.We attribute this uniform shift mainly to the temperature-dependent chemical potential shift, which is also consistent with the temperaturedependent variation of the valence band position as highlighted by the gray shaded area (see Supplemental Material for this estimation [37]).This behavior is in stark contrast to another 5d system IrTe2, where the trigonal-triclinic transition at ~280 K is accompanied by the Ir dimerization and significant d-p charge transfer, resulting in the core-level PES splitting of both Ir 4f and Te 5d [47].
The present results of core-level PES on TaTe2 thus suggest that the Ta state is strongly modified whereas the Te state remains mostly intact through the 1T"-LT phase transition.

B. Electronic band structure.
Next, we focus on the valence band structure.For simplicity, we use a set of high-symmetry points based on the primitive (virtual) 1T unit cell (see Fig. 1(e) for the (0 0 1) surface Brillouin zone (BZ)).
Here we define K /K and M /M points that become inequivalent in the 1T" phase as compared to virtual 1T. Figure 3(a) shows the ARPES intensity map at EF recorded in the high-temperature 1T" phase (300 K), obtained by using a He-discharge lamp (hν = 21.2 eV).We find the signature of multiple warped Fermi surfaces extending along the Γ -M (kx) direction, which is perpendicular to the Ta ribbon chains in the real space (i.e., the bm-axis).We note that such highly anisotropic Fermi surfaces are successfully observed because of the well-separated single domain.In the case of multi-domain samples, the signal mixing from multiple in-plane 120-degree domains should be carefully considered [18,48,49].Figure 3(b) displays the ARPES image at 300 K recorded along the Γ -K ( ) -M ( ) -Γ lines.Of particular interest relevant to the quasi-one-dimensional Fermi surface are the bands residing at the virtual 1T BZ boundaries.There are several dispersive bands that cross the Fermi level (EF) along M -K .In contrast, two relatively flat bands lie at EB ~ 0.6 and 0.9 eV along M -K .These characteristic bands, together with the quasi-one-dimensional Fermi surfaces, are very similar to those observed in the isostructural 1T"-VTe2 [18] and are also qualitatively well reproduced within our band unfolding calculation (kz = 0) as shown in Figs.3(c 3 (h).While most of the spectral weight is concentrated on the original 1T" bands, a closer comparison between ARPES and calculation [37] can also trace the additional faint band structures that are distributed with the LT (3×3) periodicity.Thus, we attribute these modifications essentially to the band-folding effect [41].On the other hand, at around M (the BZ boundary), a linear band dispersion gets strongly modified as marked by the black arrow in Fig. 3(f), which is difficult to explain by the simple band-folding effect (will be discussed later).
To further inspect the band modifications across the transition, we systematically compare the ARPES data near EF along several momentum cuts covering the 1T BZ, as shown in Figs.4(a) and 4(b).The positions of the momentum cuts #1-#7 are depicted on the Fermi surface map in Fig. 4(c).
Here, the data at 300 K [Fig. 4 These changes can be well explained by the band-folding effect and chemical potential shift described above, respectively.Rather, the most striking change is found in the intense V-shaped inner band around the BZ boundary (cuts #6, #7), centered at ky = 0.In cut #7 (i.e., K -M -K ), this 'inner' Vshaped bands transform into a pair of less-dispersive kink-like structures with about 70% decreased gradient, and their near-EF spectral intensity becomes abruptly suppressed at an endpoint momentum k1'.Indeed, as displayed in Fig. 5(d), the energy distribution curve at k1' exhibits a characteristic peak at EB ~ 70 meV (the triangle marker), which is absent in that at the Fermi momenta (k1) in 300 K.
Again, this band reconstruction goes beyond the simple band-folding effect.This is in line with a recently reported temperature-dependent optical conductivity spectrum [50], where the sudden decrease in the Drude width (i.e., scattering rate) is observed upon cooling across Ts, together with the appearance of a sharp peak at 800 cm -1 indicative of some inter-band transition.This energy (~100 meV) is close to that of the strong band reconstruction observed in the present ARPES (~70 meV), as depicted by the black triangle markers in Figs. 4

(b) and 4(d).
Here we remark on Fermi surface nesting, which has been discussed in some recent works [27,32] as the possible driving force of the 1T"-LT transition.In our ARPES results, while it is difficult to fully capture the Fermi surface topology due to the complex band structures even for 1T", we still readily identify a set of warped Fermi surfaces around |ky| ~0.4 Å -1 , as their Fermi momenta highlighted by the blue filled markers in Figs.4(a) and 4(c).This 'outer' Fermi surface is also observed in the LT phase [Fig.4(b)] with a slight increase in |ky| seemingly due to the chemical potential shift.
To examine its temperature dependence, we show in Fig. 4(d) the energy distribution curves at the Fermi momenta in cuts #5-7 (labeled as k2-k4 and k2'-k4' for 300 and 15 K, respectively), where the 'outer' bands are clearly resolved.For all spectra in both phases, the spectral weight in the vicinity of EF obeys the Gaussian-convoluted Fermi-Dirac distribution function, similar to the numerical simulation for 300 K and the experimental Au spectra at 15 K shown in the bottom of Fig. 5(d).This indicates that the 'outer' Fermi surface is retained without any gap formation at EF through the transition and is thus irrelevant to the Fermi surface nesting.Regarding the 'inner' bands (located in |ky| < 0.35 Å -1 ) including the V-shaped band at M , they are strongly modified at LT. Compared to the q-vector size of the LT (3×3) periodic lattice distortion (|qLT| ~ 0.67 Å -1 , see Fig. 1(e)), however, the length of the momentum vector connecting these 'inner' bands along the qLT direction is far short (at most ~0.4 Å -1 ).Therefore, our results do not support the simple Fermi surface nesting scenario as the origin of the 1T"-LT transition.

C. Orbital character.
Now we discuss the band orbital character.We introduce the regular octahedral coordination with orthogonal XYZ axes [see Fig. 1(c)], where the distortions in the actual TaTe6 octahedrons are omitted.This is a very simple but helpful model for capturing the band properties at the BZ boundary in the trigonal 1T-type TMDCs, based on the concept of the "hidden Fermi surface" raised by Whangbo et al. [8,51].Here, the three equivalent t2g d orbitals (dXY/dYZ/dZX) respectively form one-dimensional σbonding states along the edge-sharing octahedral network, and their combination can constitute the hypothetical Fermi surface as illustrated in Fig. 5(a).Since the σ-bonding is parallel to K-M-K, the resulting band structure exhibits a dispersive V-shape along this direction [see Fig. 5(b) for the virtual 1T-TaTe2].Though the hybridization with the chalcogen p-orbitals should be carefully considered for each case [11], this concept has been essentially demonstrated by first-principles calculations for various metallic 1T-type TMDCs [18,52,53].
The above concept can be further extended to discuss the band characters in the present 1T" and LT phases of TaTe2, as shown in Figs.5(c)-(e) and 5(f)-(h), respectively.Figures 5(c)-(e) respectively show the ARPES image, band unfolding calculation, and Ta 5d orbital-projected band calculations along K -M -K and K -M -K , obtained for the 1T" phase.The size and color of the markers in Fig. 5(e) represent the total amount of the t2g d-orbital contribution and the ratio of the XY/YZ/ZX component, respectively, at each eigenstate.As described above, the strongly anisotropic quasi-one-dimensional band structures are realized in 1T", i.e., the EF-crossing V-shaped band at M and the two flat bands at M , as marked by the green and red/blue arrows in Fig. 5(c), respectively.These bands are well reproduced by our calculations [Figs.5(d) and 5(e)] and are mainly derived from the Ta dXY and dYZ/dZX orbitals, respectively (note that the Z axis is perpendicular to the Ta chain direction, the bm-axis).It can also be recognized in the calculated partial density of states (PDOS) distributions in Fig. 5(i).Under the (hypothetical) trigonal 1T phase, the dXY/dYZ/dZX orbitals are equivalent as shown in the left panel of Fig. 5(i).As for the two-fold monoclinic 1T" [the middle panel in Fig. 5(i)], in contrast, the dYZ/dZX (red-blue curve) shows the sharp peaks at EB ~ 0.6 and 0.8 eV corresponding to the flat bands, whereas the dXY (green curve) is rather featureless in this energy region.
We note that a similar electronic structure has been already demonstrated in the sister compound (V,Ti)Te2, where the formation of the dYZ/dZX flat bands on cooling are observed at EB ~ 0.2 eV around the M point [18].There, the flat bands were discussed in terms of the localized electronic state formed by the molecular-like trimerized vanadium bonding.1T"-LT transition, whereas the dXY-derived V-shaped band at M exhibits a substantial reconstruction into unusual kink-like structures.To discuss this modification, we present in Fig. 5(j) the Ta sitespecific PDOS calculations for dXY in the 1T" and LT phases (the full set of Ta PDOS data are provided in Supplemental Material [37]).While the PDOS for Ta1/Ta2 in 1T" and Ta2A/Ta2B in LT [see Figs.1(b) and 1(c) for the site notations] exhibit the broad shape with no significant structures below EF, those for Ta1A/Ta1B in LT exhibit the multiple peak structures in a wide EB region.The peak just below EF (black arrows) partly reflects the endpoint of the kink-like band structure observed in K -M -K (the green arrows in Figs.5(f)-(h)).Hence, we suggest that the dXY orbital states of Ta1A/1B are predominantly modified through the 1T"-LT transition.
We add notes on the orbital character of the 'outer' Fermi surface discussed in Fig. 4. The band calculation in 1T" [Figs.5(d) and 5(e)] reproduces the 'outer' band near K as marked by the gray arrow.The corresponding marker sizes as displayed in Fig. 5(e) are fairly small, indicating its Te 5p-dominanted nature.The band calculations for the LT phase [Figs.5(g) and 5(h)] show that this 'outer' band crossing EF remains with similar dispersion relation, which agrees well with the experimental observations.This robustness of the Te 5p-derived state through the transition is also consistent with the temperature-independent Te 4d core-level PES spectra presented in Figs.2(d) and 2(e).

IV. Discussion and Conclusion
The present findings can be summarized as follows: (i) The core-level PES showed the temperaturedependent splitting of the Ta 4f7/2 core-level spectra through the transition (up to ~0.31 eV) in stark contrast to Te 4d5/2, suggesting the electronic reconstruction occurring predominantly on Ta sites.(ii) The temperature-dependent ARPES measurements (from 300 K to 15 K) revealed notable modifications including the sizeable chemical potential shift (~45 meV), additional (3×3)-folding of band dispersions, and the unusual kink-like band reconstruction (EB ~ 70 meV) occurring around the BZ boundary (M point) in the LT phase.(iii) Comparison with the orbital-projected band calculations indicated that the kink-like band reconstruction was primarily originated from modifications in the orbital states at the center Ta sites of the zigzag ribbons (i.e., Ta1 and Ta1A/1B), whereas the dYZ/dZXderived flat bands (around M ) and the Te 5p-dominated 'outer' Fermi surfaces remained relatively unaffected throughout the transition.These results highlight the strong orbital-selective electronic modifications in this material.Our results also rule out a simple Fermi surface nesting scenario as the origin of the 1T"-LT phase transition and may instead suggest some additional chemical bonding involving the Ta1 (Ta1A/1B) sites.Indeed, recent x-ray diffraction studies [36,54] imply the possible role of Ta-Ta chemical bonding that induces the instability of the Ta1 position.However, the mechanism that drives the transformation from the ribbon chain to the butterfly-type Ta patterns needs to be further investigated, e.g., by using the out-of-equilibrium ultrafast experiments.
Finally, we would like to discuss the inherent structural fluctuation emerging above Ts, that is relevant to the present ARPES results.According to the work by Sörgel et al. [21], the roomtemperature TaTe2 hosts an anomalously large atomic displacement parameter of Ta1 atoms along the bm-axis (i.e., U22 ~ 0.04 Å 2 , which exceeds more than twice the values of U11 and U33).This indicates that the ribbon chain pattern in TaTe2 has some prominent instability towards additional distortion, appearing as the strong fluctuation of the Ta1 atomic positions.We also point out that an unusual convex-upward electrical resistivity curve [21,24,27,28,34,50,55] as well as a broad Drude component in the optical conductivity spectrum (about 20 times broader from 300 K to 5 K) [50] are also reported (e) (0 0 1) surface Brillouin zones for 1T (gray), 1T" (cyan), and LT (orange).q 1T" and q LT indicate the q-vector of the 1T" (3×1) and LT (3×3) periodic lattice distortions, respectively.The crystal structures are visualized by VESTA [56].and 4d 3/2 , cyan rectangles).The gray shaded region shows the possible energy shift estimated from the temperature-dependent valence band measurements [37].All the data in this figure were collected with a synchrotron light source (photon energy: 90 eV).
) and 3(d).In Figs.3(e)-(h), we present the results for the low-temperature LT phase in a similar manner as in Figs.3(a)-(d).The ARPES data shown in Figs.3(e) and 3(f) are collected at 15 K.While at first glance the Fermi surface contour in Fig. 3(e) is almost unchanged from 1T" [Fig.3(a)], we observe a substantial spectral reconstruction in the band dispersion [Fig.3(f)].Along Γ -K and Γ -M , the hole-like bands split into sharp submanifolds with small energy gaps (typically 50-150 meV), as denoted by the red arrows.These features are well reproduced by our band calculation as shown in Fig.
(a)] are divided by the Fermi-Dirac distribution function convoluted with the Gaussian resolution function to remove the thermal smearing effect of the Fermi-Dirac cutoff.The cyan curves and blue circle markers in Figs.4(a) and 4(b) indicate the momentum distribution curves at EF and their peak positions (i.e., Fermi momentum), respectively.We find several types of modifications on cooling, such as band segmentation predominantly seen in cuts #1, #2, and the upward shift of the EF-crossing Λ-shaped band as depicted by the white dotted lines in cuts #3, #4.

Figures 5 (
Figures 5(f)-(h) show the band dispersions for the LT phase, in the similar manner as Figs.5(c)-(e).Although the original calculated band structure for LT (the thin curves in Fig. 5(h)) contains so many branches due to the folding, its unfolded image [Fig.5(g)] is directly comparable to the ARPES data [Fig.5(f)] and the 1T" results [Figs.5(c) and 5(d)].Both the ARPES spectra and calculations indicate that the dYZ/dZX-dominated flat bands at M are scarcely modified through the

Fig. 2 .
Fig. 2. Temperature dependence of core-level spectra.(a) Overall core-level photoemission spectra measured at 320 K.The magnified profile (×50, orange) is also shown for clarity.(b), (c) Temperature-dependent evolution of the Ta 4f 7/2 core-level intensity color map [(b)] and spectral profiles at selected temperatures [(c)].The black dotted curves in (c) indicate the fitting Voigt functions at 320 K and 20 K [37].(d), (e) Same as (b) and (c), but for the Te 4d 5/2 core-level.The orange circle markers in (d) trace the highest intensity peak positions.The spectrum at 320 K (the broken red curve) is also overlaid on the data at 20 K for comparison in (e).(f) Close-up comparison of the peak top of Te 4d 5/2 spectra (the green rectangle in (e)) at 320 K and 20 K. (g) Temperature dependence of energy position shifts (relative to the values at 20 K) for the highest intensity peak of Te 4d 5/2 (orange circles), the center of spectral weight of Ta 4f 7/2 (purple triangles) and Te 4d (including 4d 5/2

Fig. 4 .
Fig. 4. Temperature dependence of Fermi-level crossing bands.(a), (b) ARPES spectra along selected momentums (cut #1-7, shown in (c)) for the 1T" (300 K) [(a)] and LT (15 K) phases [(b)].The data of (a) is divided by the Fermi-Dirac distribution function to visualize the band structure near E F .The cyan curves show the momentum distribution curves at E F (integral width: 20 meV).The blue filled circles (at |k y | ~ 0.4 Å -1 ) trace the 'outer' Fermi surface, whereas the open circles (in |k y | < 0.35 Å -1 ) partly track the complex 'inner' Fermi surfaces.The white broken lines in cut #3, 4 indicate the Λ-shaped band that forms the small Fermi pocket.The triangle marker in cut #7 at 15 K [(b)] depicts the location of the abrupt intensity suppression of the V-shaped band.(c) ARPES intensity map at E F at 300 K (same as Fig. 3(a)) overlaid with the peak plots extracted from the momentum distribution curves at E F .(d), (e) Energy distribution curves (integral width: 0.05 Å -1 ) at selected momentums [(i)-(iv) shown in (a), (b)] at 300 K [(d)] and 15 K [(e)].The energy-resolution gaussian (FWHM of 16 meV), the simulated gaussian-convoluted Fermi-Dirac distribution function at 300 K, and the Au spectra at 15 K are also shown for reference.