Dimensionality-driven power-law gap in the bilayer TaTe₂ grown by molecular-beam epitaxy

Charge-density waves (CDWs) are characterized by a spontaneous modulation of lattice and charge orders, which translate into varied deformation patterns.^1–4 A prime example is the transition metal dichalcogenides (TMDCs), in which a wide variety of CDW distortion patterns emerge and intertwine with different quantum phases, modulating symmetry, electron correlation, and topology.^5–9 Within TMDCs, tantalum dichalcogenides (TaX₂, X = S,Se) have been a platform for investigating the role of dimensionality to the interplay between CDW and electron correlation.^10–14 As the ground state, TaS₂ is thought to host a Mott-insulating phase in both three- and two-dimensions, whereas TaSe₂ exhibits a bulk metallic phase that undergoes a metal–insulator transition at the two-dimensional (2D) limit with enhanced effective electron correlation^15–18 [see Fig. 1(a)].

In the case of tellurides, MTe₂ (M = V, Nb, Ta) crystallizes in the T″ phase (C2/m), characterized by the double zigzag chains forming the 3 × 1 × 3 superstructure with respect to the 1T (CdI₂) structure.^19–27 In particular, bulk TaTe₂ further exhibits a unique phase transition on cooling below 170 K, which breaks the double zigzag chain into Ta heptamer clusters, giving rise to the 3 × 3 × 3 low-temperature (LT) phase.^28–30 Across this phase transition, abrupt changes in the temperature (T)-dependent transport properties such as resistivity and Seebeck coefficient are reported, but the system maintains metallicity down to the lowest temperature.^28,31 The Te–Te overlaps are thought to play an important role in governing its structural and electronic properties, as the larger ionic radius of Te is responsible for the strong covalency and interlayer interactions.^32–38 Here, a substantial p–d charge transfer is known to occur, and the contribution of Te 5p at the Fermi level is expected with strong d–p hybridization. This distinguishes TaTe₂ from TaS₂ and TaSe₂, which leads to different CDW patterns and also the strength of electron correlation [Fig. 1(a)]. In this context, while dimensionality is still expected to play a major role in the electronic structure of TaTe₂, the mechanisms driving modifications are also expected to differ significantly from those of other tantalum dichalcogenides. Indeed, recent studies have reported on varied superstructures realized in low-dimensional TaTe₂, while its low-energy electronic structures are yet to be explored.^39–41 

In this work, by combining scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), we reveal the electronic structure of epitaxially grown films of TaTe₂ as thin as two layers fabricated via molecular-beam epitaxy (MBE). We evidence a characteristic suppression of the density of states (DOS) at the Fermi level in the bilayer (2L) TaTe₂, which gradually evolves at low-temperatures. From our results, we suggest that long-range Coulomb interaction and disordered CDW evolution are favored in low-dimensions and give rise to a power-law gapped state.

The morphology and structure of the TaTe₂ islands on graphene substrates are shown in Fig. 1(b), measured via in situ STM. The height profile taken along the red line in Fig. 1(b) is shown in (c), in which the estimated thickness of 1.2 nm is assigned to the 2L-TaTe₂. The profile of 1.2 nm thick 2L-TaTe₂ is uniform across different islands and reproducible across different samples. The atomically resolved STM image of the substrate is shown in Fig. 1(d), and it is consistent with the epitaxial graphene exhibiting characteristic superstructure modulation due to interaction with the SiC substrate.⁴² The atomically resolved image of 2L-TaTe₂ islands [Fig. 1(e)] shows a triangular lattice with an average periodicity of d = 3.75 Å, as estimated from the fast Fourier transform (FFT) analysis [Fig. 1(f)]. The typical dI/dV spectrum acquired on 2L-TaTe₂ is shown in Fig. 1(g), where a V-shaped dip is observed at the Fermi level (E_F). Such an electronic feature is discussed later, together with the ARPES results. The STM images taken with higher voltages (V = −0.5 V) also reveal a weak signature of a disordered charge-order-like pattern, in which the FFT analysis gives an estimation for the mean periodicity of 10.7 Å (roughly 2.8 times the periodicity of the atomically resolved image; see Fig. S1 of the supplementary material). Similar observations have also been reported in other recent work,³⁹ where similar superstructures were found in TaTe₂ thin films with low-temperature annealing. Further confirmation of the quality of TaTe₂ thin films was performed by characterization via reflection high-energy electron diffraction (RHEED) and Raman spectroscopy (see Fig. S1 of the supplementary material). We note that the bulk, ten-layer, and six-layer TaTe₂ show similar Raman spectra at room-temperature [see Fig. S1(d) of the supplementary material], in good agreement with Ref. 30. Our simulation of the Raman shift values (as detailed in methods of the supplementary material) of the bulk T″-phase also supports that the films as thin as six-layers are analogous to bulk TaTe₂.

To investigate the modification to the electronic structure of TaTe₂ with decreasing thickness, we performed ex situ ARPES measurements for bulk single-crystal, ten-layer, and two-layer thin films (Fig. 2). Figure 2(a) shows the Brillouin zone (BZ) of the 3 × 1 × 3 room temperature phase (denoted by green solid) together with the corresponding 2D BZ (denoted by red). In Fig. 2(b), the 2D BZs of 1 × 1 (black), 3 × 1 (red), and 3 × 3 (blue) are further shown. ARPES results taken with 21.2 eV photons along Γ–M₂ obtained for bulk samples at room-temperature (RT = 300 K) and low-temperature (LT = 25 K) are shown in Figs. 2(c) and 2(d), respectively. At room-temperature, we can observe hole-like bands of strong intensity centered around the Γ point, with the bottom at M₂ around 0.6 eV. At low temperatures, these bands exhibit a series of band segmentations due to the 3 × 3 superstructure. By comparing the momentum distribution curves (MDCs) taken at the Fermi level with an energy window of 50 meV [Fig. 2(e)], modification across the RT(T″)-phase to LT-phase can be clearly visualized from the shift of the Fermi momentum. In addition, bands with weaker photoemission intensity are observed with larger Fermi momentum at both room-temperature and low-temperature, as shown by the black arrows in Fig. 2(e). Our orbital projection calculation of the room-temperature phase of bulk TaTe₂ (see Fig. S3 of the supplementary material) indicates considerable orbital mixing between Ta 5d and Te 5p in these bands. Notably, various bands can be observed to cross the Fermi level at both room- and low-temperatures, with no signature of gap evolution. These features were well reproduced in the previous study.⁴³ 

Having established the overall electronic structure of bulk TaTe₂ at room- and low-temperatures, we now compare the low-temperature ARPES results for 10L- and 2L-TaTe₂ [Figs. 2(f)–2(i)]. Notably, the overall broadening of the dispersive features in film samples occurs due to the absence of in-plane orientation, as RHEED images indicate the formation of azimuthally rotated domains. Despite that, spectral features along high-symmetry lines can be expected to dominate the ARPES measurements, as demonstrated for other azimuthally disordered TMDCs.⁴⁴ Taking this into account, for 10L-TaTe₂ [Fig. 2(f)], a qualitative agreement with bulk results is observed with broad and strong intensity features centered around Γ. This is also supported by the similar dispersion acquired in the azimuthally averaged bulk TaTe₂ acquired by integrating the bulk dispersion at varied azimuth angles (Fig. S6). For 2L-TaTe₂ [Fig. 2(g)], on the other hand, the main features of the band structure are shifted toward higher binding energies with a strong reduction of intensities near the Fermi level. The MDCs taken at the Fermi level [Fig. 2(h)] help visualize the change compared to 10L films. The broad intensity distributions observed between −0.3 and 0.3 Å⁻¹ are absent in 2L-TaTe₂; instead, a remaining peak at roughly 0.42 Å⁻¹ is observed. In Fig. 2(i), the energy distribution curves (EDCs) for 2L show the transfer of the spectral weight near the Fermi level to the deeper binding energies (E_B) as compared to 10L. This unique modification in 2L-TaTe₂ was consistently confirmed in both ex situ and in situ experiments [Figs. S2(a) and S2(b)], in which the comparison of ARPES measurements indicates analogous dispersive features in both sets of experiments. Furthermore, the remaining itinerant bands in 2L-TaTe₂ [Fig. 2(h)] are noted to exhibit low intensity when compared to the main features observed at E_B = 0.5 eV. Such differences in the intensities might be rationalized by the differences between the photoionization cross section of Ta 5d and Te 5p, the former being substantially larger at 21.2 eV (approximately four times).⁴⁵ 

To further evidence the electronic structure modification, the temperature evolution of the spectral features of TaTe₂ films was examined at the Fermi momentum values. In 2L-TaTe₂, the momentum value of 0.42 Å⁻¹ was chosen to correspond to the remaining itinerant peak [Fig. 2(h) red arrow]. In 10L-TaTe₂, due to the broadness of the bulk-like features, the value of 0.24 Å⁻¹ was chosen to correspond to the edge of the broad intensity distribution [Fig. 2(h), black arrow]. The normalized EDC at 300 and 25 K of 10L and 2L films taken at the corresponding momentum values are shown in Fig. 3(a) [see Figs. S4(a) and S4(b) of the supplementary material for details of calibration and normalization]. The EDCs were obtained after dividing the ARPES data by the Fermi–Dirac distribution function convoluted with the Gaussian function, taking into account apparatus energy resolution (16 meV). In Fig. 3(a), modifications of electronic structure at low-temperatures can be observed to differ between the 10L and 2L samples. To visualize the differences in the temperature modification of the electronic structure of the fabricated films, the EDC difference between 25 and 300 K (I_25K − I_300K) for 10L- and 2L-TaTe₂ is shown in Fig. 3(b). Blue shaded areas indicate enhanced photoemission intensities at low-temperatures, whereas the red color indicates suppression of intensities. We note two characteristic temperature-dependent modifications in 2L-TaTe₂: a photoemission intensity enhancement at high binding energies (E_B > 0.1 eV) and an intensity suppression at low binding energies (E_B < 0.1 eV). In contrast to the 2L-TaTe₂, the 10L films exhibit only the high binding energy modification, with no further modification at low binding energies. To characterize the high binding energy temperature evolution in 2L-TaTe₂, we examine the EDC taken at temperatures ranging from 415 to 20 K [Fig. 3(c)]. For each curve, the peak position E_T was estimated by a polynomial fit to extract the maximum position, as denoted by the markers. The energy shift of the peak relative to the 25 K curve (ΔE = E_25K − E_T) is plotted as a function of temperature in Fig. 3(d). Notably, the peak shift evolves linearly with heating from 25 to 300 K, as highlighted by the linear fitting function.

The unique suppression of intensities at low binding energies for 2L-TaTe₂ [Fig. 3(b)] indicates the power-law gap evolving at low temperatures, resembling the V-shaped dip observed in scanning tunneling spectroscopy (STS) measurements in Fig. 1(g). To further probe the intensity suppression in 2L-TaTe₂, we examined the temperature dependence of its spectral features. The normalized and symmetrized EDC taken at k = 0.42 Å⁻¹ obtained at temperatures varying from 415 to 25 K is shown in Fig. 4(a). Here, we define the T-dependent quantity I₀(T) as the intensity taken at the Fermi level [i.e., I(E_B = 0, T)]. In addition, the result of fitting by the linear and quadratic functions is plotted on the right side (E_B < 0). The quadratic component gradually decreases in cooling, leading to the emergence of the V-shaped gap at low temperatures [I(E_B, 0) ∝ |E_B|¹]. The temperature evolution of I₀ is also shown in Fig. 4(b). On cooling, a progressively linear decrease in the I₀ is observed below around 250 K.

The ARPES results evidence a unique electronic structure and temperature-dependence for 2L-TaTe₂ in comparison with thicker films (10L). A possible hypothesis to explain the drastic electronic structure modification of 2L-TaTe₂ is the dimensionality-induced modification of the CDW phases in the group-V MTe₂. Indeed, the emergence of a multitude of CDW phases was found in the 2D group-V MTe₂, indicating the existence of metastable CDW phases that were non-existent in the bulk.^37,38,46 In the present work, STM measurements indicate the presence of a disordered superstructure in the system, as suggested by the broadened FFT peaks in Fig. S1(f). In bulk TaTe₂, previously reported STM and STS measurements show that neither 3 × 1 × 3 nor 3 × 3 × 3 phases host the V-shaped gap observed in the present work.⁴⁷ Given the correspondence between the bulk and 10L-TaTe₂ presented in Figs. 2 and S1, the modification of the electronic structure of 2L-TaTe₂ shown in Fig. 2 also suggests that such a short-range charge-order may be unique to 2L. Indeed, the energy shift of EDC toward higher binding energies at low temperatures, as evidenced in Fig. 3(c), differs from bulk TaTe₂, which exhibits a slight energy shift toward lower binding energies across the transition from T″-phase to LT-phase.⁴³ Interestingly, the temperature-dependent behavior of the higher binding energy shift (E_B = 0.5–0.4 eV) and the emergence of a power-law gap at low binding energies occur with a similar T-linear behavior, as evidenced in our ARPES measurements. There could be a mechanistic connection between the power-law gap formation and the local charge-order in 2L-TaTe₂. Despite the structural similarity with TaS₂ and TaSe₂, which exhibit a Mott metal–insulator transition as a consequence of enhanced effective electron correlation in 2D, a full gap is absent in 2L-TaTe₂. As apparent in the present ARPES on bulk, 10L- and 2L-films, TaTe₂ differs significantly from the other sister compounds, possibly due to the strong p–d charge transfer. In such cases, a simple Mott insulator picture is hardly applicable.

We argue that the power-law gap in 2L-TaTe₂ is more akin to the soft Coulomb gap in the Efros–Shklovskii (ES) model. Originally, the ES model described impurity bands of doped-semiconductors, in which long-range Coulomb interaction and disorder can give rise to a power-law gap [Fig. 4(c)].^48–52 The ES model has been discussed in other 2D TMDCs such as semimetal WTe₂⁵³ and semiconducting MoS₂,⁵⁴ but the observation of a Coulomb gap in a metallic system such as TaTe₂ is unexpected. Here, we suggest a mechanism in which the disordered charge-order produces the random charge potential, which, together with an incompletely screened long-range Coulomb interaction, would lead to a power-law gapped phase in the 2L-TaTe₂ [Fig. 4(d)]. Indeed, theoretically, itinerant systems featuring long-range interactions can give rise to a soft-gap phase of disorder analogous to the ES model.^55–57 In the ES model, the soft-gap is pinned at the Fermi level, and the density of states (DOS) in the vicinity of the gap is approximately N(E, T = 0) ∝ |E − E_F|^d−1, whereas the temperature dependence at Fermi energy in the low-T limit reads N(E_F, T) ∝ T^d−1, in which E, E_F, and d represent the energy, Fermi energy, and dimensionality of the system, respectively.⁵⁸ The temperature dependency of 2L-TaTe₂ supports this picture: both I(E_B, 0) and I(0, T) show approximately E_B- and T-linear behavior, respectively, whereas potassium deposition experiments of 2L samples show a robust power-law gap at the Fermi level (see Fig. S5 of the supplementary material). It must be mentioned, however, that the lack of azimuthal order in the film samples causes further complications since the resulting azimuth averaged spectra may smear the CDW gap into a soft-gap-like feature in the ARPES spectra. Despite that, the temperature-linear behavior observed in the 2L-TaTe₂ suggests differences with a conventional CDW picture, in which characteristic temperature and energy scales are expected along the CDW phase transition. While a more detailed investigation of the temperature behavior of both bulk and multilayer films could confirm the present scenario, we leave it for future investigations. Nevertheless, the presented ES picture allows rationalizing the emergence of the power-law gap close to the 2D limit, as adjacent layers in bulk could effectively screen the long-range Coulomb interactions. Such unscreened interactions could also contribute to the enhancement of the charge inhomogeneity showing up as the local CDW-like clusters with the help of electron–phonon interactions. We suggest that the unique energy shift (E_B = 0.5–0.4 eV) observed in 2L-TaTe₂ can be a trait of this emerging charge-order by reducing the layer number. From this perspective, the emergence of the power-law gap and the local charge-order might be effectively coupled via unscreened long-range interactions.

In conclusion, by fabricating 2L-TaTe₂ epitaxial thin films, we revealed a unique electronic phase characterized by a power-law gapped phase. By employing STM and ARPES, we demonstrate the presence of a power-law gap at the Fermi level and its evolution with temperature. The spectral suppression at the Fermi level is reminiscent of a soft Coulomb gap that appears in random systems. We argue that such behavior might be a product of the strongly disordered CDW and unscreened long-range interactions, providing a system analogous to the ES model. Such unscreened Coulomb interactions are particularly relevant in the 2D limit, giving rise to a power-law gap with glass-like charge ordering.