Pressure-induced metallization and superconducting phase in ReS2

Among the family of TMDs, ReS2 takes a special position, which crystalizes in a unique distorted low-symmetry structure at ambient conditions. The interlayer interaction in ReS2 is rather weak, thus its bulk properties are similar to that of monolayer. However, how does compression change its structure and electronic properties is unknown so far. Here using ab initio crystal structure searching techniques, we explore the high-pressure phase transitions of ReS2 extensively and predict two new high-pressure phases. The ambient pressure phase transforms to a"distorted-1T"structure at very low pressure and then to a tetragonal I41/amd structure at around 90 GPa. The"distorted-1T"structure undergoes a semiconductor-metal transition (SMT) at around 70 GPa with a band overlap mechanism. Electron-phonon calculations suggest that the I41/amd structure is superconducting and has a critical superconducting temperature of about 2 K at 100 GPa. We further perform high-pressure electrical resistance measurements up to 102 GPa. Our experiments confirm the SMT and the superconducting phase transition of ReS2 under high pressure. These experimental results are in good agreement with our theoretical predictions.


INTRODUCTION
The transition metal dichalcogenides (TMDs) MX 2 (M, transition metal; X, chalcogen, S, Se, Te) have become a topic of current interest in recent years due to their unique structural, electronic, optical, and tribological properties. [1][2][3][4][5][6][7][8][9][10][11][12] Up to now, there are approximately more than 60 TMDs reported, and most of them have a layered structure resembling graphite, although these layers are actually different. In the layers of TMDs, a transition metal atom layer is sandwiched by two chalcogen atom layers, forming a X-M-X sandwiched structure. The X-M-X trilayers then stack together via weak van der Waals (vdW) interaction, resulting in the different phases in TMDs such as 1T, 1T′, 2H c , 2H a , and 3R. [12][13][14][15][16][17] Due to their unique layered structure, TMDs exhibit some exceptional functional properties under pressure such as superconductivity 3, 18-20 and charge density wave (CDW). 6,[21][22][23] Moreover, as a result of the weak interlayer interactions, similar to graphite, their bulk materials can be cleaved easily into monolayer, forming a new class of two-dimensional materials with many novel properties. 24,25 For example, these cleaved monolayers can be reassembled layer by layer with a specified sequence to form programmed heterostructures and devices. 26 Using socalled "vertical" techniques, such vdW heterostructures with unique properties have been fabricated recently. 27,28 More interestingly, compared with the bulk form, monolayer and few-layer TMDs generally exhibit distinct electronic structure and optical properties. 29 For example, the bandgaps of some semiconducting TMDs will change from indirect to direct in a single layer. 25,27 Among the family of TMDs, ReS 2 occupies a special position and has received incremental attention recently. 30,31 Unlike most of the TMDs, the ambient ReS 2 crystallizes in a distorted CdCl structure with low triclinic symmetry 32,33 (space group: P-1, although this structure was usually named as 1T′ in the previous literatures, to describe the structural evolution of ReS 2 clearly, as discussed later, we name this ambient structure "distorted-3R" in this paper). The lowsymmetry structure and the distortion of Re and S atoms were related to the Peierls mechanism, 31, 34 which prevents ordered stacking and minimizes the interlayer overlap of wave functions. Thus, the interlayer interaction in ReS 2 is rather weak, and the bulk properties are similar to those of monolayer. 31,35 For instance, the direct-to-indirect bandgap transition as reported in MoS 2 is not observed in this material when going from the monolayer to bulk. 31 Since the electronic and optical properties do not change so much in ReS 2 with increasing layers, applying stress and pressure becomes an important approach to modify its properties. Generally speaking, pressure can directly modify the lattice parameters, and change effectively its electronic structures and optical properties. And pressure can also symmetrize the structure and remove the Peierls distortion. Furthermore, as a member of TMDs, metallization, CDW, and possible superconductivity under pressure can also be important issues. Among above-mentioned issues, the key point is to figure out the structural evolution of ReS 2 under pressure. In the previous work, Hou et al. 36 have explored the high-pressure structures of ReS 2 up to 51 GPa using synchrotron X-ray diffraction (XRD); they found an indication of the occurrence of a new high-pressure phase at 11 GPa. Kao et al. 37 also found a transition in ReSe 2 at the pressure of 10.5 GPa. However, both of them did not resolve the crystal structure of the high-pressure phases. In this paper, using efficient crystal structure search methods combining with ab initio calculations, we predict the evolution of the structural and electronic properties of ReS 2 under pressure. Two new high-pressure phases are identified, and the structural characteristics and their stability, electronic structure, and metallization of ReS 2 under pressure are investigated systematically. We also perform high-pressure electrical transport measurements up to 102 GPa, which confirm our predictions on the metallization and superconductivity very well. Unlike the most TMDs that undergo a phase transition from H c to H a under pressure, we find that ReS 2 has a different phase transition sequence under pressure. In addition to the known structure types of 3R, 1T, 4H and 1T, several new crystal structures of TMDs family have been proposed in our work. Our results reveal that pressure plays an important role in modifying and symmetrizing the crystal structure in the distorted TMDs system indeed.

RESULTS
Structure predictions were carried out with simulation cells containing 1−8 formula units of ReS 2 under pressure from 0 to 200 GPa. The experimentally observed ambient structure (distorted-3R phase) was successfully reproduced at 0 GPa, validating our methodology. To get accurate results, vdW interaction is taken into consideration. The optB88 functional together with the vdW-DF corrections 38 as implemented in Vienna ab initio simulation package (VASP) was applied during calculating the enthalpy pressure, due to their good performance in the layered TMDs. 39 The enthalpy data of the typical known structures in TMDs and our predicted ones are shown in Fig. 1a. Compared with the experimental lattice parameters of the ambient distorted-3R structure, the optB88 + vdW-DF functionals gives errors within only 3%, indicating that this computational setting can give good descriptions of vdW forces in ReS 2 (Supplementary Table S1). To double check the stability of the newly found structure, we also calculate its enthalpy relative to the distorted-3R phase using local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) Generalized gradient approximation (GGA) exchange-correlation functionals without vdW corrections, which is shown in the inset of Fig. 1a. At about 0.1 GPa, a new energetically favorable structure with the same triclinic symmetry (space group: P-1, we name it "distorted-1T") is uncovered, and the supercell of this structure is shown in Fig. 1b. Although the phase transition pressure changes from 0.4 GPa for LDA to 3 GPa for PBE, we can conclude that the newly found structure becomes more energetically favorable than the ambient distorted-3R structure above pretty low pressure and is stable in a wide pressure range to about 90 GPa. After that, a tetragonal I4 1 /amd structure is found to be more preferable. The detailed structural parameters of these two predicted phases are summarized in Supplementary Table S2. The calculated phonon dispersions of these two newly found phases are shown in Supplementary Fig. S1. It is shown that both phases are dynamically stable proved by the absence of any imaginary phonon frequency in the whole Brillouin zone (BZ). The volume changing with pressure is also calculated, as shown in Supplementary Fig. S2. With increasing pressure, the volume changes of distorted-3R and distorted-1T are slightly different, while a discontinuous volume change occurs in the transition from distorted-1T to I4 1 /amd, which exhibits a first-order phase transition.
The newly found distorted-1T has the same space group with the experimentally observed ambient distorted-3R, both belong to P-1; however, their packing is different. During optimizing these two structures under higher pressure, we find that the previously known ambient pressure P-1 structure tends to symmetrize into the 3R structure (space group: R-3m), while the new P-1 structure found in this work tends to symmetrize into the 1T structure (space group: P-3m1), respectively, (Figs. 1b, c). That is the reason why we think it is more proper to name the known ambient P-1 structure as "distorted-3R", although it is usually called "distorted-1T" or 1T′ in the literature before. Correspondingly, the newly found P-1 structure in this work is named as "distorted-1T" for the same reason. Interestingly, the 3R and 1T structures were reported in other TMDs such as MoS 2 . For MoS 2 , 1T phase is metastable and metallic, 14,15 while 3R phase is semiconducting and it keeps stable under high pressure and high temperature. 16,17 The main difference between the 3R and 1T is the stacking sequence of the S-Re-S trilayer. Different from 3R phase, all Re atoms in 1T phase share the same (x, y) coordinate. The 3R structure can transform to the 1T structure with a relative sliding between sandwiched layers. From the analysis above, one can find that the layer-sliding might also be responsible for the transition from the distorted-3R to distorted-1T phase. In fact, similar layer-sliding has been observed in other TMDs under pressure such as MoS 2 , which leads to the transition from 2H c to 2H a , 13 while in WTe 2 , it is from Td to 1T′ and finally 2H. 39 Previously, Hou et al. 36 have explored ReS 2 up to 51 GPa using X-ray diffractions (XRD) with a wavelength of 0.4959 Å, and reported a high-pressure phase at around 11 GPa, which is stable at least up to 51 GPa. However, they did not resolve the crystal structure of this high-pressure phase because of the peak broadening and overlapping. According to the experiment, the phase transition is indicated by the remarkable change of the (220) peak, the relative intensity of which considerably increased when the phase transition occurred. In Fig. 2, we show the simulated XRD curves of distorted-3R and distorted-1T structures together with the experimental results at 11 and 50 GPa, respectively. As one can see, the XRD curves of our predicted distorted-1T structure agree well with the experimental results. Particularly, the remarkable change of the special peak during the phase transition matches the experimental results nicely. We find that, if using a longer X-ray wavelength, for instance, λ = 1.54056 Å, to simulate the XRD curves, the XRD patterns of distorted-3R and distorted-1T structures will show more difference and are easy to be distinguished, especially for the peaks between 35 and 40°( see Supplementary Fig. S3a for more details). Furthermore, as shown in Supplementary Fig. S3, the lattice parameters of these two P-1 structures show different trends, indicating that they have quite different anisotropies under pressure. However, the experimental results indicate that the new phase emerges at around 11 GPa, which is higher than our theoretical transition pressure. The difference might be due to a large activation barrier for the phase transition.

DISSCUSSIONS
The distortion of S and Re atoms in the distorted-3R phase was believed to be related to the Peierls mechanism. 34 The distortion reduces the band energy from electrons, while increases the repulsion energy between the atoms. However, if the decrease of the band energy is sufficient enough to overcome the cost in increased repulsion, the distorted low-symmetry structure can exist stably. Generally speaking, pressure tends to destroy the Peierls distortion, and leads to high-symmetry structure. To reveal the origin of the atoms distortion in the distorted-1T structure, we show the total density of states (DOS) of the distorted and undistorted 3R and 1T phases at 15 GPa in Figs. 3a, b. It can be seen that the distortion introduces a bandgap in both 3R and 1T structures, as this greatly decreases the band energy. Particularly, we notice that, through the layer-sliding, the first peak of total  Fig. 3 The electronic band structures and density of states (DOS). a The total electronic DOS of various structures at 15 GPa, which clearly shows that the distortions in distorted-3R and distorted-1T structures introduce bandgaps, which can be attributed to the Peierls mechanism. b The total and partial DOS for the distorted-1T ReS 2 at 15 GPa. The Fermi level is set to zero. c The first Brillion zone and d the calculated band structures of the distorted-1T ReS 2 at several pressures. The distorted-1T undergoes a metallization transition with a band overlap mechanism upon compression Pressure-induced metallization D Zhou et al DOS below the Fermi level in distorted-1T phase is lower than that of distorted-3R phase, thus the distorted-1T phase decreases more energy than the distorted-3R phase. Therefore, we can see that the Peierls mechanism still plays an important role in the newly found distorted-1T phase. The partial density of states (PDOS) of distorted-1T phase at 15 GPa are also shown in Fig. 3b, both the valence band maximum (VBM) and the conduction band minimum (CBM) are mainly derived from hybridized Re-d and Sp states, while other states such as S-s, S-d, and Re-p have negligible contributions to the VBM and CBM.
We further investigate the band structure of distorted-1T phase at different pressures. The spin-orbit interactions are taken into account during the band structure calculations, see Fig. 3d in details. At 15 GPa, both the VBM and CBM are located at the Q point, so it is a direct bandgap semiconductor at 15 GPa, and the bandgap is about 0.66 eV. As pressure increases, the lowest line of the conduction band moves down, the eigenvalues at the B point and the one between the Z and Γ points reduce quite a bit. Both of them become lower than the state at the Q point, leading to a transition from direct gap to indirect gap at about 60 GPa. Upon further compression, the distorted-1T structure undergoes a semiconductor-metal phase transition at about 70 GPa, which results from the closure of the bandgap. The detailed changes of the bandgap with pressure are shown in Supplementary Fig. S4.
Under higher pressure, a new three-dimensional highly compact phase with the tetragonal I4 1 /amd symmetry is predicted to be more energetically stable, taking the place of sandwichlayered structures, see Fig. 4a in details. From the band structure and total DOS shown in Fig. 4c, we can see that the tetragonal I4 1 / amd phase is strongly metallic. Moreover, the metallic character of this structure is mainly contributed by the Re-d states with fewer contributions from the S-p states. We further calculate the electron-phonon coupling (EPC), phonon spectra, partial phonon density of states, Eliashberg EPC spectral function a 2 F (?), and the electron-phonon integral λ(ω) at 100 GPa of this phase with the density functional perturbation theory, 40 which are shown in Fig. 4d. We find the EPC constant λ to be about 0.41. The estimated critical temperature superconductivity (T c ), using the Allen-Dynes equation 41 with μ * = 0.1 is about 2 K, which agrees with our experimental results reasonably well as discussed later. From the calculation of the phonon linewidths, it can be seen that the intermediate-and high-frequency S vibrations make a significant contribution to the overall EPC constant. The PDOS, Eliashberg EPC spectral function a 2 F (ω), and the electron-phonon integral λ(ω) also confirm this result. It seems that S atoms may be vitally important to the superconductivity of ReS 2 .
To experimentally confirm the predicted semiconductor-semimetal phase transition and the superconducting phase, we investigate the evolution of resistance as a function of temperature for ReS 2 single crystal under high pressure up to 102.0 GPa in Fig. 5. At 4.0 GPa, ReS 2 exhibits the semiconducting conductivity similar to its ambient pressure behavior. With increasing pressure up to 11.0 GPa, the overall resistance significantly decreases by two orders of magnitude. Especially at 15.1 GPa, a non-semiconducting behavior emerges above 100 K, where the resistance is almost independent of temperature, which could be attributed to the pressure-induced structural transition from distorted-3R to distorted-1T as mentioned above. The pressure-induced metallic conductivity can be recognized under 32.0 GPa in the high-temperature range, while the resistance at low temperature still keeps the semiconducting profile. Note that the semiconducting profile preserves till 70.0 GPa, as shown in Fig. 5b, which implies that the ground state is indeed semiconducting in nature. Only when the pressure is further enhanced to 81.0 GPa, the semiconducting behavior is almost completely suppressed. The characteristic pressure could also be traced in the pressure dependence of isothermal resistance shown in Fig. 6a, where a small change of slope takes places around 70 GPa, in well agreement with the theoretically predicted semiconductor-metal phase transition in the distorted-1T structure. Fig. 4 The crystal structure, band and electron-phonon coupling of the I4 1 /amd ReS 2 . a The crystal structure of I4 1 /amd at 100 GPa. b The first Brillion zone and c the calculated band structure of I4 1 /amd ReS 2 at 100 GPa. d The calculated phonon dispersions of I4 1 /amd ReS 2 at 100 GPa. The size of the dots represents the phonon linewidth of each mode. Partial phonon DOS, Eliashberg EPC spectral function a 2 F(ω), and the electron-phonon integral λ(ω) are also shown on the right panel More interestingly, in accordance with the electron-phonon calculations, when the pressure reaches to 91.0 GPa, a small drop in the resistance curve appears around 2.5 K, as shown in Fig. 5c. The resistance drop becomes more and more pronounced with increasing pressure up to 102.0 GPa, the limiting pressure in our experimental set-up. To make sure that the drop of the resistance is indeed a superconducting transition, we carry out electrical resistance measurements under various external magnetic fields aligned along c-axis of ReS 2 at 102.0 GPa. As seen from Fig. 6b, the resistance drop is gradually suppressed and moves towards low-temperature curve with the increasing field up to 1.0 T. The Ginzburg-Landau fitting yields a critical field of 2.509 T, as shown in the inset of Fig. 6b. The suppression of resistance drop by magnetic field thus confirms the presence of pressure-induced superconductivity. The failure to observe zero resistance is most likely to be caused by the non-hydrostatic compressive stress, which results in a huge pressure gradient in the sample. To achieve zero resistance in the superconducting phase with the critical temperature around 2 K, both higher-pressure and lowertemperature limit should be reached. Upon pressure releasing   Supplementary Fig. S5, which is accompanied by the increasing normal state resistance.
In summary, we have explored the ground-state structures of ReS 2 under pressure systematically using crystal structure prediction methods combining with ab initio calculations. Based on structural evolution, we think it is more proper to name the ambient P-1 structure "distorted-3R", although it is usually called as 1T′ in the literature. Upon very small compression, the ambient distorted-3R is predicted to transform to a new triclinic distorted-1T structure with the same P-1 symmetry. The simulated XRD patterns of this new phase agree well with the previous experimental XRD results under pressure. The layer-sliding is found to be responsible for the transition, and from the electronic structures, we find the Peierls mechanism playing an important role in decreasing the energy of the low-symmetry structures in ReS 2 . Moreover, through high-pressure transport measurements, ReS 2 is confirmed to undergo transitions from semiconductor to metal under pressure. Under higher pressure, a new highly compact metallic phase with tetragonal I4 1 /amd symmetry becomes stable above 90 GPa, which has a critical superconducting temperature of about 2 K at 100 GPa. This work shows that pressure plays a vital part in changing and symmetrizing the crystal structure in the distorted TMDs system, which also leads to dramatic modifications on its electronic structures, such as band closure and superconducting transition.

Ab initio calculations
Structure prediction through a global minimization of free energy surfaces has been successfully applied to predict high-pressure structures. [42][43][44][45][46] Here we extensively searched for ReS 2 ground-state structures under pressure based on the CALYPSO (Crystal structure Analysis by Particle Swarm Optimization) method. 47,48 Besides, another structure searching method, ab initio random searching 49, 50 was used to cross-check the reliability of the most stable structures at selected pressure. The structural optimization and electronic structure calculations were performed within the framework of the density functional theory using the generalized gradient approximation PBE, 51 as implemented in the VASP. 52 The well-established allelectron projector-augmented wave method 53 was adopted with 2p3s and 4s4p5s4d as valence electrons for S and Re atoms, respectively. For the structure searching, relatively economic computation criteria such as a plane-wave basis kinetic energy cutoff of 400 eV and a grid of spacing 2π × 0.06 Å −1 for BZ sampling were found to be sufficient. While the enthalpy and electronic structure calculations were performed at a higher level of accuracy, which consists of 800 eV for the kinetic energy cutoff and a kpoint grid spacing of 2π × 0.025 Å −1 . The phonon calculations are carried out through direct or so-called supercell approach, as implemented in the phonopy code. 54 The full-potential linearized augmented plane-wave method implemented in WIEN2K code 55 was used to compute the band structure of the distorted-1T and I4 1 /amd structures at selected pressure points. The EPC was calculated using the QUANTUMESPRESSO code. 40 The ultrasoft Vanderbilt pseudopotentials with a PBE 51 exchange-correlation functional were used. We choose 45 Ry for the kinetic energy cutoff of the plane-wave basis after testing the convergence. The k-space and q-point integrations over BZ were performed on a 12 × 12 × 12 grid and a 4 × 4 × 4 grid, respectively.

High-pressure experiments
The high-pressure resistance measurements were carried out in a screwpressure-type diamond anvil cell made of BeCu alloy. The diamond culet was 200 μm in diameter. A rhenium gasket was preindented from a thickness of 200 to 30 μm, which was drilled in center by pulsed laser ablation. A mixture of epoxy and fine cubic boron nitride (cBN) powder was added to the pit, and then compressed firmly to insulate the electrodes from the gasket. The cBN-covered pit served as a sample chamber. Then, a plate-like single crystal with the dimension of 70 × 15 × 5 μm 3 was loaded into the pit without any pressure-transmitting medium. A 5 μm-thick platinum foil was used for the electrodes with a standard four-electric-probe method. Some ruby powder was placed on the top of the sample and served as pressure markers. Pressure at room temperature was then calibrated by the ruby fluorescence scale below 70 GPa 56 and the diamond Raman scale above 70 GPa, 57 respectively.