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 dichalcogenide 1T-TaS2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}, 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-TaS2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}. 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. Mott insulation and charge density waves are fascinating phenomena which alter the electronic structure of a system and occur via the complex interplay of a number of different parameters. Here, the authors use scanning tunnelling microscopy to investigate the localised changes in the electronic state near the insulator-metal transition of 1T-TaS2 and find that strain may play a role.

F or 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 Mottgap 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 Fig. 1a, the SOD cluster is formed by 13 Ta atoms with 12 surrounding Ta atoms shrinking to the central Ta. At the CCDW state, the SODs are regularly arranged to form a ffiffiffiffiffi 13 p ffiffiffiffiffi 13 p 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, with each bright spot representing a SOD. Consistent with the ffiffiffiffiffi 13 p ffiffiffiffiffi 13 p reconstruction, the bright spots form a triangular lattice of SODs and the distance of two neighboring SODs is measured to be 12.1 Å. A single unpaired 5d electron of the central Ta atom in each SOD contributes to the half-filled electronic band, leading to the Mott insulator state of the pristine 1T-TaS 2 . In the field of view (FOV) in Fig. 1b, a differential conductance (dI=dV) spectrum is measured at each point in a dense grid of spatial positions. The average spectrum is shown in Fig. 1c. With the spectrum proportional to the electronic density of states (DOS), the sharp coherence peaks at 240 mV and −200 mV correspond to the upper and lower Hubbard bands (UHB and LHB), 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. Fig. 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 nanometer-sized 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 Figs. 2 and 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.
Electronic states in mosaic domains. to '5', the differential conductance at −200 mV decreases, the Mott gap is suppressed to a V-shaped gap, and the V-shaped gap develops together with a finite DOS at zero bias (Fermi energy E F ). A V-shaped gap has been observed in Cu intercalated 1T-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. Figure 3a shows a topographic image of the corrugated surface, from which we could observe a periodic and triangular lattice of SODs without any domain wall. This FOV is within a single domain. Bright and dark stripes appear roughly along the diagonal direction, representing a corrugated surface with a modulation of z-axis height. We focus on a straight line across central stripes (the white arrowed line in Fig. 3a). In Fig. 3b, the surface height is drawn as a function of distance along the line, in which the ups and downs correspond to the bright and dark stripes in the two-dimensional topograph. A flat surface is shaped into a corrugation with parallel ridges and grooves. The height of the corrugation is in the range of tens of picometers, comparably small as that of other stain-induced corrugations [44][45][46] . 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. Figure 3e, f 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.

Discussion
A Mott insulator-metal transition can be generally explained by a reduced ratio of U=W in the one-band Hubbard model. The change of U can be represented by a change of the Mott gap. For the linecut spectra in Fig. 3c, we fit both UHB and LHB peaks of each spectrum with a Gaussian function (Supplementary Fig. 5) and extract their energy positions and bandwidths. As shown in Fig. 4, the bandwidth of LHB is consistently larger than that of UHB, indicating a higher hopping constant t for LHB (t is proportional to W). When approaching the groove from the left side, we could observe that the Mott gap gradually decreases while the bandwidth of both UHB and LHB peaks is nearly unchanged (brown region). Here, the decrease of U is mainly responsible for the reduced U=W. When being closer to the groove (purple region), the VB gradually merges with LHB and the LHB bandwidth rapidly increases. The increase of UHB bandwidth is accompanied by the development of in-gap state and the Vshaped spectrum. Although U still decreases in this region, the increase of bandwidth is observed to be the dominant factor to reduce U=W. In ref. 15 , a multi-orbital Hubbard model has been proposed, including contributions both from the central Ta orbital and the edge orbital of surrounding Ta atoms. With the one-band Hubbard model as a down-folded version of the multi-orbital model, the reduction of U=W is explained to be both from the decrease of U (of central Ta orbital) and from the decrease of on-site energy difference between two orbitals. The change of U can be represented by a change of the Mott gap, and the on-site energy difference between two orbitals can be represented by the relative position between VB and LHB peaks. Consistent with this twoorbital model, our observation reveals that the rapid increase of W happens together with the mergence between VB and LHB, which is the main factor to reduce U=W and induce a metallic state. The smooth spectrum evolution in our corrugated surface provides a clear picture of how the Mott insulator-metal transition gradually happens. A Mott-gap 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). 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 Figs. 7 and 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 expected to bring a tensile strain to the glued sample. Instead of corrugations, cracks are the dominant features on the surface for samples glued on the SiO 2 (0001) substrate. The precise position of the Mott-gap collapse cannot be simply concluded from the height profile of corrugations. The atomicresolved topography is required for the microscopic analysis of the strain distribution in a corrugation, which is however technically challenging. Therefore to answer how or whether the strain as an underlying mechanism tunes the Mott-gap collapse is still beyond our current capabilities. Nevertheless, the observation of the similar behavior in the 'strained sample' suggests that the stable mosaic state and the corrugation can be generated as a response to the strain.
The mosaic state is a very complex phenomenon. Following we discuss possible roles of strain for the mosaic state. For the mosaic state, an energy cost is required to create domain walls. Strain may help to overcome the energy barrier for the creation of domain walls. Then the mosaic state can be initially generated as a response to the strain. Other techniques like laser pulse or tipcurrent pulse can similarly help to create domain walls and mosaic state in this material. No matter how the mosaic pattern is created, the metallic state in mosaic pattern can be similarly related with the destruction of the long range CCDW order. 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 wall underneath the top layer, thus cannot provide evidence for the stacking order proposal. A single uniform domain 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 2 . The smooth evolution of spectrum in corrugated surface provides a clear picture of how the Mott gap collapses. The mosaic state and the corrugation is further confirmed in the 'strained sample'. A controllable strain engineering should be explored in the future to tune the electronic phases of 1T-TaS 2 .

Methods
Sample preparation. The high quality 1T-TaS 2 single crystals were grown by the chemical vapor transport (CVT) method with iodine as the transport agent. Ta (99.99%, Aladdin) and S (99.99%, Aladdin) powders with mole ratio of 1:2 were weighted and mixed with 0.2 g of I 2 , which were placed into silicon quartz tubes. These tubes were sealed under high vacuum and heated for 10 days in a two-zone furnace, where the temperature of source and growth zones were fixed at 850°C and 750°C, respectively. Then the quartz tubes were removed from the furnace and quenched in ice water mixture.
STM measurement. The STM and STS experiments were carried out in a commercial STM system 51 . The samples were gradually cooled to liquid nitrogen temperature and in situ cleaved. An electrochemically etched tungsten tip was treated with e-beam sputtering and field emission on a single crystalline with an Au (111) surface. A constant current scanning mode maintained by a feedback loop control was used in this experiment. The dI=dV spectra were taken with a standard lock-in technique with a frequency of 983.4 Hz and an amplitude of 10 mV. The dI=dV spectra at domain walls were taken with a bias modulation of 2 mV. All data were acquired at liquid helium temperature (~4.5 K) except for special statement.

Data availability
The source data and related supporting information are available upon reasonable request from the corresponding author.