Evolution of the Fermi Surface of 1T-VSe₂ across a Structural Phase Transition

Abstract

Periodic lattice distortion, known as the charge density wave, is generally attributed to electron–phonon coupling. This correlation is expected to induce a pseudogap at the Fermi level in order to gain the required energy for stable lattice distortion. The transition metal dichalcogenide 1T-VSe₂ also undergoes such a transition at 110 K. Here, we present detailed angle-resolved photoemission spectroscopy experiments to investigate the electronic structure in 1T-VSe₂ across the structural transition. Previously reported warping of the electronic structure and the energy shift of a secondary peak near the Fermi level as the origin of the charge density wave phase are shown to be temperature independent and hence cannot be attributed to the structural transition. Our work reveals new states that were not resolved in previous studies. Earlier results can be explained by the different dispersion natures of these states and temperature-induced broadening. Only the overall size of the Fermi surface is found to change across the structural transition. These observations, quite different from the charge density wave scenario commonly considered for 1T-VSe₂ and other transition metal dichalcogenides, bring fresh perspectives toward correctly describing structural transitions. Therefore, these new results can be applied to material families in which the origin of the structural transition has not been resolved.

1. Introduction

Two-dimensional (2D) layered transition metal dichalcogenides (TMDCs) display a variety of electronic, magnetic, and transport properties, making them extensively studied materials [1,2]. Among the many TMDCs, 1T-VSe₂ gained special attention as one of the few van der Waals (vdW) materials hosting a three-dimensional charge density wave (3D-CDW) phase [3,4,5,6]. The structural distortion sets in at a transition temperature (T^*) of 110 K, presenting a 4a × 4a × 3c periodic superlattice [3,4,5,6]. Electronically, the CDW phase manifests with a pseudogap at the Fermi level and a Fermi surface nesting along the CDW wave vector [7].

In spite of the apparently universal agreement on a CDW mechanism in VSe₂, its direct experimental evidence is far from compelling. Early photoemission experiments from 1T-VSe₂ interpreted a shift of a secondary peak located just below the Fermi level as an indication of a gap opening [8,9], although a complete spectral weight suppression at the Fermi level was absent below T^*. In this approximation, the gap size was estimated to be between 20 meV to 50 meV. More recently, high-resolution angle-resolved photoemission spectroscopy (ARPES) experiments, however, did not report an energy gap around the M(L) point of the Brillouin zone [10,11,12], where spectral distortions are expected to be stronger due to coincidence with the CDW wave vector. On the other hand, a small gap of 12 meV was detected by scanning tunneling spectroscopy (STM) [13]. However, it was found to be more pronounced around the $\Gamma$-point rather than at the M-point where the Fermi surface nesting is actually expected. Additional evidence for the CDW transition is a warping effect in the band dispersions along the k_z direction of the 3D Brillouin zone [9,14,15,16,17,18]. Although this appears to be a well-established experimental result, it has never been tested for temperatures above T^*, making its relation to the CWD doubtful. In conclusion, the available experimental evidences present important inconsistencies with each other and with expected nature of a CDW phase.

Finally it may be worth mentioning that the topological surface states have recently been revealed for VSe₂ [19], implying a different Fermi surface from previous predictions and measurements. Furthermore, resolving the Dirac cone in VSe₂ is not a straightforward experiment, possibly explaining some of the inconsistencies in the previous studies. Thereby, the structural transition in VSe₂ has to be readdressed in order to investigate its impact on the electronic structure.

Here, we revisit the surface electronic structure of 1T-VSe₂ aiming to investigate the CDW phase. ARPES results virtually identical to the previous reports are reproduced using linear horizontal (LH) polarized light. However, electronic states, which have not been observed previously, are probed by linear vertical (LV) polarized light. The latter bands contribute to the Fermi surface and need to be considered for an accurate description of the CDW phase. Their inclusion yields a distinct picture of the k_z electronic dispersion, completing earlier band structure characterizations. In particular, the Fermi surface warping, usually attributed to the CDW phase, is found to be temperature independent and results from the distinct k_z dispersion of these multiple bands present at the Fermi level. On the other hand, a prominent effect associated with the CDW phase is found in the shrinkage of the electron pocket centered at the $\overline{M^{\prime }}$ point at 100 ∓ 5 K. This observation is in excellent agreement with transport measurements. Hence, the new findings in this work clarify many of the ambiguous observations present in the current literature while providing the band structure origin of the transport anomalies of 1T-VSe₂.

2. Materials and Methods

Single-crystal 1T-VSe₂ samples from 2dsemiconductors (Scottsdale, AZ, USA) were prepared through the floating zone method. The dimensions of the samples used in this work were around 1.5 × 1.5 × 0.3 mm. ARPES and core-level experiments were performed at 21-ID-1 (ESM) with a beamline of NSLS-II using a DA30 Scienta electron spectrometer (Scienta Omicron, Uppsala, Sweden). The base pressure in the photoemission chamber was 1 × 10⁻¹¹ Torr. The energy resolution was better than 12 meV, and the beam spot size was approximately 5 ${\mu }^2$. The synchrotron radiation incidence angle was 55^∘. Analyzer slit was along the M–$\Gamma$–$M^{\prime }$ direction during the ARPES measurements at normal emission and was parallel to the M–$M^{\prime }$ direction during the zone corner scan. LV polarized light was parallel to the sample surface and analyzer slit while LH polarized light was on the incident plane.

High-angle annular dark-field imaging scanning tunneling electron microscopy (HAADF-STEM) images were acquired with a Hitachi HD2700C (Hitachi, Tokyo, Japan) dedicated STEM with a probe Cs corrector operating at 200 kV at room temperature. TEM lamella were prepared using the in situ lift-out method on the Helios 600 NanoLab DualBeam FIB, with final Ga+ milling performed at 2 keV. Scanning tunneling microscopy (STM) (omicron VT-STM-XA 650 (Scienta Omicron, Uppsala, Sweden)) experiments were performed in an ultrahigh vacuum system with a base pressure of 2 × 10⁻¹⁰ Torr at room temperature. The STM images were observed in constant current mode using Pt/Ir tips. TEM and STM images were analyzed using the Gwyddion-2.55 software package. HAADF-STEM and STM experiments were conducted at the Center for Functional Nanomaterials, Brookhaven National Laboratory. Micro low-energy electron diffraction ($\mu$LEED) experiments were performed with the X-ray photoemission electron microscopy/low-energy electron microscopy (XPEEM/LEEM) end station of the ESM beamline (21-ID-2). The X-ray diffraction (XRD) experiment was carried out on the ISR beamline, 4-ID, with a wavelength of 1.079 Å. A Dectris 1M area detector was used with a Huber six-circle diffractometer to obtain detailed reciprocal space maps of the crystal.

3. Results

The crystal structure of 1T-VSe₂ was examined through multiple techniques to confirm the high quality of the samples and consistency with earlier studies. A ball–stick representation of the atomic structure is shown in Figure 1a. 1T-VSe₂ crystallizes with an in-plane hexagonal geometry as shown in µLEED and STM images given in Figure 1b,c. Both data indicate the presence of a single domain phase without extra diffraction spots or other in-plane atomic arrangements. A representative high-resolution transmission electron microscope (TEM) image further confirms the layered structure along the c-axis of the crystal with well-defined atomic layers and smooth interfaces between the monolayers (Figure 1d). XRD data in Figure 1e assign the in-plane and out-plane lattice constants of 3.354 and 6.097, respectively, in excellent agreement with the earlier reports [5]. The rocking curve of the high-quality single crystal was 0.4 degrees full width at half maximum with negligible secondary crystal grains. Finally, the chemical environment of the sample was probed by Se 3d and V 2p core-level spectra, which showed no additional spectral features beyond the spin-orbit splitting components (Figure 1f,g). The binding energies corresponded to −2 and +4 oxidation states for Se and V atoms, which is consistent with a single chemical phase in the material [20].

The surface electronic structure of a 1T-VSe₂ bulk sample is shown in Figure 2 for LH (upper panel) and LV (lower panel) polarized lights. The LH Fermi surface exhibits ellipsoidal pockets centered at the M($M^{\prime }$) points and an intense spectral feature in the zone center due to Se 4p-atomic orbitals (Figure 2a). The electronic structure along the M–$\Gamma$–$M^{\prime }$ direction looks identical to the previous reports [8,9,10,11,12,13,14,15,16,17,18]. However, the Fermi level momentum distribution curve (MDC) given above the spectrum shows weak shoulders, indicating the presence of two distinct bands close to the Fermi level (see dashed pink and yellow lines in Figure 2b). One, resembling the band structure calculations [17,18], bends into a flat dispersion towards the $\Gamma$-point and overlaps with the Se 4p-derived bands. The other instead continues the upward dispersion, crossing the Fermi level before reaching the center of the zone. Here, the former is the topological surface state of which the details can be found in Reference [19].

The electronic structure along the K–$\Gamma$–$K^{\prime }$ direction is shown in Figure 2c. The V-3d-derived bands start with a flat dispersion in the vicinity of the zone center and bend upward, crossing the Fermi level at k_‖ = −0.6⁻¹ and 0.65⁻¹. Furthermore, an intense V-shaped band characterizes the region along the K–$\Gamma$–$K^{\prime }$ direction (Figure 1d). This is the main region of interest for the CDW, where the gap is expected to be more prominent.

The spectra taken with LV polarization are presented in the bottom panels of Figure 2. The main difference between the Fermi surfaces with LH and LV polarization is that now only a point-like feature is observed at the $\Gamma$-point, facilitating the analysis of the energy-momentum maps. Along the M–$\Gamma$–$M^{\prime }$ direction, the crossing of the bands at the Fermi level is now more easily identified. Furthermore, along the K–$\Gamma$–$K^{\prime }$ direction, two small electron pockets (marked with yellow dashed lines) are additionally resolved at k_‖ = −0.45⁻¹ and k_‖ = 0.54⁻¹, respectively. More importantly, the ARPES spectrum taken along the K–$\Gamma$–$K^{\prime }$ direction shows multiple bands, marked with dashed red and yellow lines, crossing the Fermi level (Figure 2h). They can be better distinguished in the MDC given at the top of the spectrum. The observation of the multiple bands touching the Fermi level around the M point is a novelty of the present study. Therefore, this work provides a crucial component of the electronic structure to draw a correct picture of the CDW phase in 1T-VSe₂.

Up to now, the most solid evidence for the 3D-CDW phase in 1T-VSe₂ was given by the warping effect on the Fermi surface along the k_z direction [9,14,15]. However, the observation of distinct states with LH and LV polarized lights encourages re-investigation this issue with both polarizations. It is also worth emphasizing that previous photon energy-dependent ARPES experiments were not performed as a function of temperature, clearly an essential factor for ascertaining the electronic origin of the phase transition. Therefore, such an experiment is presented in Figure 3. Figure 3b–d shows the k_z dispersion for states at the Fermi level in the $\overline{ML{L}^{\prime }{M}^{\prime }}$) plane measured with LH polarization. At 10 K, far below the T^*, the results are very similar to the those shown in the literature. In particular, the pronounced asymmetries between the right and left sides around the $M\left(L\right)$-points—the so-called warping effect—were attributed to the CDW-induced Fermi surface nesting [9,14,15]. However, the k_z-dispersion taken at 160 K, well above the T^*, is essentially identical to the one from 10 K, featuring the same ‘warping’ along the k_z-direction (Figure 3c). These modulations of the spectral intensity or dispersion, therefore, cannot be attributed to the phase transition, and their origin must be searched for elsewhere. A hint comes from the dispersion map constructed with LV polarized light (Figure 3d). This reveals a more complex picture, featuring additional bands, best captured in the splitting resolved at certain photon energies. The observed asymmetric dispersion behavior in the photon energy dependencies can therefore be simply explained by the presence of multiple states close to the Fermi level combined with their photon energy-dependent photoemission cross-sections.

The above findings also suggest that the CDW-induced gap should be studied with both LH and LV polarization. For LH polarization, the ARPES spectrum taken at 85 eV along the $\overline{M}$–$\overline{M^{\prime }}$ direction is given in Figure 3e together with selected energy distribution curves (EDCs) taken below (10 K) and above (160 K) the T^* in Figure 3f. Clearly, the EDCs exhibit no gap openings at the Fermi level in this case. Similar experiments for LV polarization are shown in Figure 3g–i. Although multiple bands are captured close to the Fermi level with LV polarization, neither of them displays a prominent gap at the Fermi level (Figure 3i).

The detailed band structure characterizations given above convincingly demonstrate that the previous observations stem from multi-band crossing of the Fermi level rather than the CDW phase transition. This implies that the impact of the structural distortion on the electronic structure of 1T-VSe₂ remains an open question. On the other end, although the Fermi surface does not display gaps and nesting based on the ARPES experiments, transport measurements show clear anomalies around 110 K [21,22,23,24]. In some cases, structural transitions can cause modifications of the Fermi surface area [25,26,27,28]. Therefore, it seems sensible to investigate the size of the ellipsoidal electron pockets centered at the $\overline{M^{\prime }}$ point as a function of temperature. A Fermi surface portion covering two Brillouin zone centers is given in Figure 4a. Here, two relevant quantities are $\Delta$k, measuring the distance between the ellipsoidal pockets along the ${\Gamma }_1$–${\Gamma }_2$ direction, and $\Delta$$k_{\overline{M^{\prime }}}$, measuring the size of the pocket along the red line shown in Figure 4a. Representative spectra below and above T^* are given in Figure 4b–e), where $\Delta$k and $\Delta$$k_{\overline{M^{\prime }}}$ are also marked. Plots of these two quantities as a function of temperature are presented in Figure 4f,g. Interestingly, both $\Delta$k and $\Delta$$k_{\overline{M^{\prime }}}$ undergo a sizable change across the CDW temperature, indicating a decrease in the Fermi surface area with the temperature decreasing from 160 K or 10 K. This result is in excellent agreement with the transport measurements, which show a relative increase of the in-plane resistivity across the same temperature [21,22,23]. Therefore, this finding establishes a direct connection between the electronic structure and the structural distortion in 1T-VSe₂. Furthermore, a fluctuation larger than the error bars is observed in $\Delta$ks around 100 K. Recently, the surface electronic structure in 1T-VSe₂ was shown to host topologically non-trivial surface states [19]. Therefore, the bulk band crossing the Fermi level will have a spectral contribution from these states. Topological surface states are expected to have smaller electron–photon coupling compared to the bulk bands due to their localization in the surface region. Therefore, the sudden changes in $\Delta$k could be related to this difference, although the direct correlation is not clear at this point.

4. Conclusions

A detailed study of the electronic structure of 1T-VSe₂ has been conducted to assess the electronic origin of the CDW phase. The new ARPES data reveal the presence of previously undetected states located in the vicinity of the Fermi level and, therefore, necessarily relevant to the physical properties of 1T-VSe₂. However, no gap opening at the Fermi level is observed in correspondence with the CDW temperature. Furthermore, previous claims of a connection between the Fermi surface profile along the k_z direction and a 3D-CDW in 1T-VSe₂ are also ruled out. On the other hand, a change in the size of the in-plane Fermi surface across the CDW transition is firmly established, in good correspondence with the transport results.

A remaining issue in our work is to determine to what extent this Fermi surface ’breathing’ is or should be considered in relation to the structural transition. Either a shift of the bands or a change in the effective masses would cause such Fermi surface modifications. Based on our initial studies and analyses, both are playing role. Unfortunately, the broadening of the bands at higher binding energies and the weak modifications observed in the electronic structure prevent the establishment of an accurate conclusion at this point. It is likely that these issues can be overcome with the higher energy resolution achieved by laser-based ARPES experiments. One striking perspective of the current observation is their possible connection with the analogous Fermi surface shrink commonly observed in Fe-based superconductors [24,25,26,27]. It is believed that a nematic transition pushes the bands up or down depending on its orbital character, leading to a band splitting and consequent Fermi surface modifications [28]. In this case, it may be possible to drive 1T-VSe₂ into a superconducting state by playing with its Fermi surface shrinking. Indeed, recent observations on the superconducting properties of the 1T-VSe₂ under high pressure [29] or growth conditions [30] could be related to the results presented here.