Electronic Topological Transition in Ag2Te at High-pressure

Recently, Ag2Te was experimentally confirmed to be a 3D topological insulator (TI) at ambient pressure. However, the high-pressure behaviors and properties of Ag2Te were rarely reported. Here, a pressure-induced electronic topological transition (ETT) is firstly found in Ag2Te at 1.8 GPa. Before ETT, the positive pressure coefficient of bulk band-gap, which is firstly found in TIs family, is found by both first-principle calculations and in situ high-pressure resistivity measurements. The electrical resistivity obtained at room temperature shows a maximum at 1.8 GPa, which is nearly 3.3 times to that at ambient pressure. This result indicates that the best bulk insulating character and topological nature in Ag2Te can be obtained at this pressure. Furthermore, the high-pressure structural behavior of Ag2Te has been investigated by in situ high-pressure synchrotron powder X-ray diffraction technique up to 33.0 GPa. The accurate pressure-induced phase transition sequence is firstly determined as P21/c → Cmca → Pnma. It is worth noting that the reported isostructural P21/c phase is not existed, and the reported structure of Cmca phase is corrected by CALYPSO methodology. The second high-pressure structure, a long puzzle to previous reports, is determined as Pnma phase. A pressure-induced metallization in Ag2Te is confirmed by the results of temperature-dependent resistivity measurements.


Results
With increasing pressure, the first and the second pressure-induced structural transitions of Ag 2 Te occur at 2.2 and 11.3 GPa, respectively, which are illustrated in Fig. 1 by the onsets of new peaks. Based on the decompression data, all structural phase transitions are reversible. As can be seen in Supplementary  Fig. S1(a,b), Rietveld refinement of ADXRD patterns indicate that the P2 1 /c phase is retained up to 2.0 GPa. By comparing our Supplementary Fig. S2 with Fig. 1 and Supplementary Fig. S3 in ref. 24, it is clear that our ADXRD patterns of Cmca phase are distinct different with those of previous report in intensity sequence of peaks such as (202), (023), (204), and (221) in 3.2-9.5 GPa region. Moreover, a bad fitting result was obtained, when the previously proposed structure of Cmca phase was used to carry out Rietveld refinement. So, in order to determine the crystal structure of this phase, the structure prediction via CALYPSO methodology 28 was performed and a corrected structure of Cmca phase was obtained. The corrected structure can result in a good Rietveld fitting (see Supplementary Fig. S3), and the detailed refinement result is shown in Supplementary Table S1. The distinct difference between the corrected structure and the reported structure is mainly in the internal coordinates of atoms. On the other hand, as shown in Supplementary Fig. S4(a), the pattern is well fitted by a combination of P2 1 /c and Cmca phase at 2.2 GPa, and the inset indicates that the (023) characteristic peak of the Cmca phase can be observed at 2θ = 13.7°, which is ignored by Zhao et al. The detailed refinement result for 2.2 GPa are located in Table 1. From Supplementary Fig. S4(b) and the inset of it, it is clear that the first transition is not completed up to 2.6 GPa. Thus, the XRD pattern of 2.4 GPa, measured by previous report, in fact represents mixed structures of P2 1 /c and Cmca phase rather than an isostructural P2 1 /c phase 24 . When the pressure increase, the second structural transition emerged at 11.3 GPa with a new peak marked at 2θ = 14.3°, and the characteristic peak (marked by asterisk) of the second high-pressure phase become gradually stronger as the pressure increases to 19.2 GPa (see Supplementary Fig. S5(a,b)). By the known structures of A 2 B compounds 23 , the long-puzzling high-pressure phase has been assigned to an orthorhombic structure (space group Pnma, No.62). The diffraction data of 25.5 GPa can be well fitted by coexistence of Cmca and Pnma phase, as shown in Supplementary Fig. S6, and the detailed refinement result can be found in Table 2. The second high-pressure phase transition is not finished up to 33.0 GPa, the highest pressure measured here.
The schematic representation of the high-pressure phase transition sequence for Ag 2 Te is located in Supplementary Fig. S7. It is indicated that the structure of the P2 1 /c phase is built up of stacking layers of  Supplementary Table S2. It is obvious that Ag-Te bond lengths of Cmca phase all decreased under pressure. During the transition process from P2 1 /c phase to Cmca phase, Ag1 atoms experience shear glide along b axe, leading to the formation of layered rectangle network (see Supplementary Fig. S8(a,b)). As shown in Supplementary  Fig. S8(c), the layered Ag1 atom network which are located in bc plane undergo shear glide along c axe, inducing the layered zigzag network to become flat. It can be seen from Supplementary Fig. S8(d), due to glide takes place in Ag2 atom chain along b direction, layered rhombus network of Ag2 atoms are formed when the phase transition occur. As shown in Supplementary Fig. S8(a), thanks to the glide of Ag2 atom chain, the marked Te-Ag2 bond length decreased from 3.896(4) Å to 2.954(6) Å, which result in the [TeAg8] coordination polyhedron developed to [TeAg9] coordination polyhedron via the phase transition. In the second phase transition process, the layered rectangle network of Ag1 atoms become to layered square network, and the layered rhombus network of Ag2 atoms become to layered rectangle network (see Supplementary Fig. S8(a,b,d)). Moreover, the [TeAg9] coordination polyhedron chains undergo shear glide when Cmca phase transforms to Pnma phase, in Supplementary Fig. S8(c).
As shown in Fig. 2(a), all the lattice parameters including angle β in the P2 1 /c phase monotonically decrease with increasing pressure. The linear compressibility of the different axes in the P2 1 /c phase are κ a = 0.0664(3) GPa −1 , κ b = 0.0230(7) GPa −1 , and κ c = 0.0314(3) GPa −1 , respectively. It can be seen that  (7) - x Te 0.2758 (8) 1.0000  the b and c axes are less compressible, which is due to Ag1 atoms are all located in bc plane, as shown in Supplementary Fig. S8(b), bringing in stronger Ag1-Ag1 interaction. As shown in Fig. 2(b), all the lattice constant ratios display notable changes in compressibility near 1.8 GPa. By taking into account that the ETTs, a modification of the topology of the Fermi surface, are verified by the changes in compressibility of the lattice constant ratios in other TIs-Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 25 , the above abnormal changes may be ascribed to an ETT around 1.8 GPa.
The presence of active lone electron pairs (LEPs) can result in the asymmetry of coordination polyhedron 12,29 . Here, the variance of Ag-Te distances, K, is used to quantify the distortion of coordination polyhedron 30 . Based on the Ag-Te distances of P2 1 /c phase in Supplementary Table S2, the pressure dependence of K in P2 1 /c phase is shown in the Supplementary Fig. S9(a). It can be seen that K undergoes an intense fluctuation around the pressure where ETT happens, indicating an increase in the LEP stereochemical activity before 1.8 GPa and the LEP activity experience an intense decrease above that pressure. Therefore, the ETT may be related to the change of the LEP activity from the chalcogen lone-pair p orbital 31 and the existence of the weaker interlayer interaction 32 . As shown in Supplementary  Fig. S8(b), Ag1 atoms are located in ab plane of Cmca phase, which results in stronger Ag1-Ag1 interaction. Therefore, a and b axes of Cmca phase are less compressible than c axe, see Supplementary Fig.  S9(b), with κ a = 0.0174(5) GPa −1 , κ b = 0.0144(4) GPa −1 , and κ c = 0.0336(6) GPa −1 . This is unlike the previous result that a axe was reported more compressible than b and c axes 24 . As shown in Supplementary  Fig. S9(c), the linear compressibility of the different axes in the Pnma phase are κ a = 0.0136(6) GPa −1 , Supplementary Fig. S10 shows the pressure-volume (P-V) relationships of the P2 1 /c, Cmca and Pnma phase. These P-V data are fitted to the usual Birch-Murnaghan (BM) equation of state (EOS) 33 .
where B 0 is the bulk moduli and ′ B 0 is the pressure derivative. The ′ B 0 were fixed at 4 for all the phases. We obtain B 0 of 66.48(7) GPa (V 0 = 67.78(2) Å 3 ) for the P2 1 /c phase, B 0 of 76.89(8) GPa (V 0 = 65.84(0) Å 3 ) for the Cmca phase, and B 0 of 99.03(0) GPa (V 0 = 62.93(9) Å 3 ) for the Pnma phase. Mulliken population analysis has indicated that the population of Ag-Te covalent bond for Cmca phase is larger than that for P2 1 /c phase, which suggests that the larger B 0 of Cmca phase comes from the stronger Ag-Te covalent bond. Moreover, it can be seen from Supplementary Table S2, Ag-Te bond length of 2.816(6) Å in Cmca phase is smaller than that of P2 1 /c phase, suggesting that the stronger Ag-Te covalent bond may result from the smaller Ag-Te bond lengths. The bulk moduli of high-pressure phases are different with that of previous report, which is due to the fact that the reported isostructural P2 1 /c phase is not existed and the reported structure of Cmca phase is corrected. In order to check on the change of topological nature and the assumption of a pressure-induced ETT in Ag 2 Te near 1.8 GPa, we performs high-pressure resistivity measurements which is believed as an effective supplementary mean for ADXRD measurements to identify electronic structural phase transition. Figure 3 shows the pressure dependence of resistivity for Ag 2 Te at room temperature. The electrical resistivity for Ag 2 Te at 1.8 GPa is nearly 3.3 times to that at ambient pressure, then the electrical resistivity presents a intense collapse and decreases relatively slowly beyond 2.0 GPa. Above ADXRD results have proved that there is no structural transformation until 2.2 GPa. This distinct change may come from ETT 34 . Therefore, in order to shed light on the notable change in the P2 1 /c phase around 1.8 GPa, we carried out first-principles calculations, which is useful to investigate the effects of pressure-induced ETT on the electronic band structures and may discover the development of topological nature on Ag 2 Te. However, Zhao et al. performed first-principles calculation on P2 1 /c and Cmca phase in order to study the pressure-induced metallization.
As shown in Fig. 4(a,b), bulk Ag 2 Te is an indirect band-gap semiconductor at ambient pressure and at 1.0 GPa, with the valence-band maximum (VBM) located around D point and the conduction-band minimum (CBM) at Γ point. However, as shown in Fig. 4c, Ag 2 Te is a direct band-gap semiconductor at 2.0 GPa with VBM and CBM at Γ point. At ambient pressure, the band inversion of surface states at Γ point is the origin of the topological nature, as discussed by Zhang et al. 6 . The partial electron density of state (PDOS) and sum DOS results of Ag 2 Te at ambient pressure, 1.0, and 2.0 GPa, respectively, indicate that VBM are mainly composed by the hybridization of Ag-4d and Te-5p electrons, as shown in Fig. 4(d-f). The orbital composition is almost invariant under selective pressures. This indicates that the TI character should be stable under pressure 26 . On the other hand, it is found that the increasing interlayer spin-orbit coupling and the fluctuation of LEP activity 35 under pressure caused a positive pressure coefficient of indirect band-gap and a reduction in the direct band-gap at Γ point, which result in an indirect-to-direct transition 36 . Given this indirect-to-direct transformation of Ag 2 Te, the above assumption of a pressure-induced ETT appears reasonable 25,37 .
Moreover, the resistivity as a function of temperature at various fixed pressures was shown in Fig. 5(a). Before ETT, it is noticed that the resistivity decreases with increasing temperature, demonstrating specific semiconductor behaviors. From Fig. 5(a), the bulk insulating character of Ag 2 Te becomes better and better with increasing pressure, which is a good agreement with our electronic band structure results. As shown in the inset of Fig. 5(a), the resistivity displays a positive relationship with increasing temperature at 4.1 GPa, which implies that the Cmca phase performs a metallic behavior. Therefore, the pressure-induced insulator-metal transition was experimentally confirmed by the temperature-dependent resistivity results. The carrier activation energy could be obtained by linearly fitting the plots of lnρ versus 1000/T 38 . As shown in Fig. 5(b), there is a continued increase in the carrier activation energy with increasing pressure, indicating a development of carriers energy barriers, which induces that the transport of 3D carrier becomes harder and harder by applying pressure. Therefore, at 1.8 GPa, the best bulk insulating character is obtained, which is the best topological nature of Ag 2 Te by applying pressure.

Discussion
For applying the technological devices with 3D TIs, one of the most important goals is the control of the 2D electrical conduction in the surface of these materials 25 . Therefore, TIs should exhibit a good bulk insulating character. However, rather high bulk conductivity was observed in most of the TI samples, due to a high concentration of free 3D carriers caused by defects and/or impurities 25 . For Ag 2 Te in this work, before ETT, due to bulk band-gap enhanced under pressure, a decrease of 3D electron concentration can be obtained, resulting in an increase of bulk resistivity, in Fig. 3. Thus, for Ag 2 Te, it is verified that pressure is helpful for suppressing bulk conductivity and revealing the relative contribution of surface states conductivity 25 . So, a better topological nature of Ag 2 Te was obtained by compression. The electronic band structures of Ag 2 Te around ETT are different. And the differences are as follows: (a) The CBM and VBM show higher curvature after ETT, and a lower effective mass is expected 26 . (b) Due to indirect-to-direct band-gap transition, Ag 2 Te becomes a direct band-gap semiconductor after ETT, which is unique for 3D TIs, being a better candidate for infrared detection 4,39 . (c) After ETT, the CBM and VBM of bulk states are both located at Γ point, which is same as that of surface states, causing a reduction in the separation between surface states and bulk states in the momentum space. However, on the contrary, after ETT, the separation is further enhanced for Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 20,21,26 .
In addition, for 3D TIs family, we suggest that the pressures, at which the ETTs occur, are strongly sensitive to carrier concentration and Fermi energy level of the samples, due to charge concentration easily affect the competition between interlayer interaction and LEP activity, which could cause diverse pressure-induced behaviors and properties 25,32,40 . For example, in previous report, the resistivity of Ag 2−δ Te decreased continuously as pressure increased to 1.0 GPa, and showed a positive pressure coefficient beyond that pressure 41 . For purchased sample of Sb 2 Se 3 12 , the Raman study did not reproduce the pressure-induced ETT, but it can be observed in single crystal grown by Bridgeman method 42   particular, for Bi 2 Te 3 , different hole concentration could give rise to the observations of pressure-induced superconductivity differing by 3-6 GPa 20,33 , and the pressure-induced ETT did not appear in n-type samples 45 .
Besides, we would like to mention about the experimental evidences to detect the appearances of pressure-induced ETTs in 3D TIs, as follows. (a) In this work, the pressure-induced ETT is related to the change of the LEP activity which can result in the asymmetry of coordination polyhedron 29 . (b) By means of the changes of the lattice constant ratios, Raman frequencies and Raman linewidths, pressure-induced ETTs have been revealed in Bi 2 Te 3 , Bi 2 Se 3 and Sb 2 Te 3 , which indicated both XRD measurements and Raman scattering measurements are sensitive methods to evidence the presences of ETTs in this family 25 . (c) Due to the ETTs are shown to strongly influence the thermoelectrical properties of samples, the ETTs can be easily probed by the changes of thermoelectrical properties in 3D TIs 25,46,47 . Thus, an improvement of thermoelectrical property can be expected in Ag 2 Te after ETT. (d) For both Bi 2 Se 3 and Ag 2 Te, pressure-induced ETTs can affect the pressure coefficients of resistivity 27 . Based on the change in pressure coefficients of resistivity, we determine that the best topological nature of Ag 2 Te can be seen at 1.8 GPa.
Finally, in order to apply the technological devices with 3D TIs, it is important to obtain a TI with a good topological nature, which has a large band-gap and low bulk charge density 25 . Since, for TIs family, the positive pressure coefficient of bulk band-gap is only found in Ag 2 Te, it is necessary to perform systematic studies on Ag 2 Te under compression, which may provide us an approach of enhancing bulk band-gap of 3D TIs. Thus, some suggestions are as follows: different stoichiometric Ag 2±δ Te, impurity doping, non-hydrostatic pressures and low temperature measurements could be available experimental plans to induce expected electrical transport properties and TI with a good topological nature under pressure. Angle Resolved Photon Electron Spectroscopy technique should be used to reveal the metallic surface states of Ag 2 Te upon pressure. Low-temperature electrical transport experiments are expected to discover topological superconductor states of Ag 2 Te.

Methods
Room-temperature angle-dispersive X-ray diffraction. Ag 2 Te powder was provided by Yuan et al. 48 . For high-pressure diffraction measurements, the sample was crushed in a mortar with a pestle. As shown in Supplementary Fig. S11, our diffraction rings pattern is clear. EDX result of powder sample was located in Supplementary Fig. S12. Measurements were performed in a Mao-Bell type DAC with 4/1 methanol/ethanol mixture as the pressure medium. The powder was loaded in a 120 μ m diameter hole drilled in the T-301 stainless steel gasket and chips of ruby were added as pressure calibrator 49 . The ADXRD experiments were performed using a synchrotron angle-dispersive x-ray source (λ = 0.6199 Å) of the 4W2 High-Pressure Station of Beijing Synchrotron Radiation Facility (BSRF). Patterns were fitted by Rietveld refinement, using the General Structure Analysis System (GSAS) and graphical user interface EXPGUI package 50 .
High-pressure resistivity measurements. Van der Pauw electrodes were integrated on one diamond anvil for in situ resistivity measurement under high pressure 51 . The temperature dependence of resistivity measurements was conducted by placing the DAC into a tropical drying cabinet, lasting for more than 10 min to make the thermal balance.
First-principles calculations. We performed structure prediction through a global minimization of free energy surfaces merging ab initio total-energy calculations via CALYPSO methodology 28 . The geometric optimization were performed using density functional theory with the Perdew-Burke-Ernzerhof exchange-correlation as implemented in the Vienna Ab initio Simulation Package (VASP) code 52 and the generalized gradient approximation (GGA) 53 is implemented on a projector augmented wave (PAW) basis 54,55 . Integration in the Brillouin zone was performed using special k points generated with 5 × 8 × 5 mesh parameter grids. Convergence tests give a kinetic energy cutoff as 550 eV and spin-orbit coupling interaction was included through the calculation.