Possible strain induced Mott gap collapse in 1T-TaS2

Tuning the electronic properties of a matter is of fundamental interest in scientific research as well as in applications. Recently, the Mott insulator-metal transition has been reported in a pristine layered transition metal dichalcogenides 1T-TaS$_2$, with the transition triggered by an optical excitation, a gate controlled intercalation, or a voltage pulse. However, the sudden insulator-metal transition hinders an exploration of how the transition evolves. Here, we report the strain as a possible new tuning parameter to induce Mott gap collapse in 1T-TaS$_2$. In a strain-rich area, we find a mosaic state with distinct electronic density of states within different domains. In a corrugated surface, we further observe and analyze a smooth evolution from a Mott gap state to a metallic state. Our results shed new lights on the understanding of the insulator-metal transition and promote a controllable strain engineering on the design of switching devices in the future.

metal transition hinders an exploration of how the transition evolves. Here, we report the strain as a possible new tuning parameter to induce Mott gap collapse in 1T -TaS 2 . In a strain-rich area, we find a mosaic state with distinct electronic density of states within different domains. In a corrugated surface, we further observe and analyze a smooth evolution from a Mott gap state to a metallic state. Our results shed new lights on the understanding of the insulator-metal transition and promote a controllable strain engineering on the design of switching devices in the future. * yiyin@zju.edu.cn 1 arXiv:2005.13311v1 [cond-mat.str-el] 27 May 2020 For a half-filled electronic band, strong correlation of electrons can lead to a unique Mott insulator state, when the ratio of Coulomb repulsion U to the bandwidth W (U/W ) exceeds a critical value [1]. Proximity to the Mott insulator is the origin of many exotic superconducting states, such as in cuprates [2], magic-angle graphenes [3,4] and transition metal dichalcogenides [5][6][7]. To explore the superconducting mechanism, it is important to understand the Mott insulator state and how the transition evolves from a Mott insulator to a metallic or superconducting state [8].
In this study, we show a possible strain-induced Mott-gap collapse in the pristine 1T -TaS 2 by scanning tunneling microscopy (STM). In a strain-rich area, we find mosaic CDW domains and the stable mosaic state is most possibly induced by the intrinsic strain. In the mosaic state, we could detect variable spectra from a Mott gap state to a metallic state within different domains. We further find a corrugated surface, also possibly a strain-induced feature. When being across the corrugation, a smooth evolution of the Mott-gap collapse is observed and analyzed. The Mott gap is suppressed gradually and a V-shaped metallic state emerges at the corrugation. In the process of Mott-gap collapse, the rapid increase of bandwidth W is found to be the dominant factor to reduce U/W . By gluing 1T -TaS 2 on the organic-glass substrate, we introduce strain to the sample surface at low temperature, and confirm the strain-induced mosaic pattern and corrugation. Our results provide a further understanding of the Mott insulator-metal transition and suggest the strain engineering as a possible new tuning method to modulate the Mott insulator state.

Results
Crystal structure and electronic state of the pristine 1T -TaS 2 . The unit structure of 1T -TaS 2 is composed of a triangular lattice of Ta atoms sandwiched between two layers of triangular lattice of S atoms. With an ABC-type stacking, each Ta atom is coordinated octahedrally by S atoms. The sample is at near commensurate CDW (NCCDW) state at room temperature and develops to the CCDW state at around 170 K ( Supplementary Fig.   1). A basic element of the CDW state is the so called Star of David (SOD). As shown in reconstruction [36][37][38]. With the single crystal sample cleaved and a top S layer exposed, the STM experiment is performed on the exposed surface at liquid helium temperature around 4.5 K.
A typical topography is shown in Fig. 1b  respectively [11]. Energy positions of UHB and LHB result in a Mott gap of 440 ± 20 meV.
In the average spectrum, there is also a broad peak at -460 mV and a kink feature at 440 mV, corresponding to the valence band (VB) peak and the conduction band (CB) peak of the CDW gap, respectively [11,39]. All these characteristics are consistent with previous reports of the pristine 1T -TaS 2 [15,24,25,39,40].
Stable mosaic state in a strain-rich area. We intentionally look for a strain-rich area. Figure 1d is a topographic image of a 100 nm × 100 nm area. The complex morphology indicates a strain-rich environment around this area, which may originate from the cleavage process. A zoom-in image of the white box shows a mosaic state with several nanometersized domains (Fig. 1e). The textured domains are different from the quasi-hexagonal phase in the NCCDW state [41,42]. The pattern shows that they are more similar to the voltage pulse induced mosaic state [24,25]. Within each domain, the superlattice of SODs is still preserved. Neighboring domains are separated by bright domain walls, across which there is a translational phase shift of the CDW order. We do not see any rotational shift of the CDW order between different domains [15]. This mosaic state is stable at 4.5 K, without any change after a longtime measurement. With the temperature increased to 60 K (Fig. 1f), the domain wall pattern is almost the same as that at low temperature (see more details in Supplementary Fig. 2 and Supplementary Fig. 3). Different from the metastable mosaic state triggered by a voltage pulse [24,25], this mosaic state in strain-rich area is very stable, possibly attributed to the intrinsic and stable strain. TaS 2 , and the gap gradually disappears with the increase of temperature [17]. A similar V-shaped gap has also been observed in isovalent Se doped 1T -TaS 2 [15].
The variation of dI/dV spectra is consistent with the conductance map in Fig. 2a, in which the domain marked by '1' is represented by a bright white patch and different from other purple patches. We notice that the conductance is relatively uniform within each domain in Fig. 2a, and the periodic pattern in the domain is still consistent with the CCDW superlattice. For conductance at E F , both a zero conductance and a finite conductance are observed in the dI/dV spectra in Fig. 2c, with the latter representing a metallic state (olive and blue curves). Within each single domain, the zero bias conductance at the clean area is also homogeneous, as shown in Fig. 2d. Some of the bright features in Fig. 2b are due to the CDW impurities like missing or distorted SOD. Other bright patches in Fig. 2b aggregate at the step edge and the edge of each domain. There may be a mechanism that leads to trapped carriers at the edges of domains, which is however not clear yet.
Mott-gap collapse at a corrugation. The mosaic domains and related complex electronic states are speculated to be induced by the intrinsic strain. We further find an area with a corrugated surface, not far away from the strain-rich area ( Supplementary Fig. 4). The corrugation is also a possible strain-induced feature [43,44]. In this corrugated area, we observe a smooth evolution of Mott-gap collapse across the corrugation, which gives us a special example to analyze the Mott insulator-metal transition. Without an atomic resolution in this experiment, we cannot make a quantitative analysis of the strain based on precise determination of atomic displacement [34,46].
We measure a series of dI/dV spectra along the straight line, with data shown in Fig. 3c.
Some typical spectra are selectively chosen and shown in Fig. 3d. The location of each spectrum is labeled by a colored dot in the height profile (Fig. 3b). Approaching the dark groove from both sides, we could observe a smooth evolution of Mott-gap collapse. Both UHB and LHB peaks move gradually toward the zero bias (Fermi energy E F ), with peak height decreases and peak width increases. The energy range of zero conductance shrinks until an in-gap state develops to form a metallic V-shaped spectrum. From the smooth evolution of spectra, we can track how the Hubbard band peaks evolve when approaching the groove. In the metallic state, the Hubbard band peaks are separated from two V-spectrum peaks. In Fig. 3c, another important feature is that the VB peak moves toward the zero bias together with the LHB peak, and finally merges to form the V-shaped spectrum.
To check the detailed distribution of the Mott-gap collapse in this corrugated area, we choose a framed area in Fig. 3a and measure the dI/dV spectra at a dense array of locations. Figures 3e and 3f show conductance maps at -200 mV and 0 mV, respectively. Consistent with previous linecut spectra, metallic state in the shallow groove corresponds to a dark depression in Fig. 3e and a bright protrusion in Fig. 3f. In contrast, the Mott insulator state outside the groove shows a strong LHB peak (bright color in Fig. 3e) and a zero conductance around the Fermi energy (dark color in Fig. 3f). An additional metallic state at the left bottom corner in Fig. 3f may be due to the complex trough there, as indicated by the large depression at the same position in Fig. 3a. collapse could also happen on the intrinsic domain walls [40,47,48], which is however a sharp transition that we cannot obtain a similar analysis as in Fig. 4 (see Supplementary Note 1).

Discussion
The single domain in the topographic image of the corrugated surface also proves that this Mott-gap collapse is a new phenomenon different from that induced by the domain-wall.
We also find another corrugation at this sample, which shows similar Mott-gap collapse at the corrugation ( Supplementary Fig. 6). The mergence of the VB and LHB is reproduced at this corrugation. We further conducted experiment on the 'strained sample' by gluing 1T -TaS 2 on the organic glass substrate. With a large thermal expansion coefficient of the substrate, a compressive strain is expected to act on the sample at low temperatures. The mosaic state and the corrugation are both confirmed in the 'strained sample' (Supplementary Fig. 7 and Supplementary Fig. 8). We also conducted the experiment on samples glued on the SiO 2 (0001) substrate, which has a rather small thermal expansion coefficient and is Afterwards, a global strain may possibly make the domain pattern energetically stable. A strain can tune the electronic states while preserves the overall flat atomic plane [34], like the rather weak spatial height modulation within the mosaic state. Another proposal to explain the mosaic state is that the stacking order tunes the Mott insulator-metal transition [24,25].
The stacking order is variable according to the SOD misalignment along the crystalline c axis [49,50]. In this experiment, we did not observe any domain walls underneath the top layer, thus cannot provide evidence for the stacking order proposal. A single uniform domain 7 of Mott insulator state exists in the strain-rich area (Fig. 2), which may be related with the stacking order effect.
In conclusion, we have carefully studied the strain-induced corrugation and mosaic state in 1T - TaS  Data availability. The source data and related supporting information are available upon reasonable request from the corresponding author.