Introduction

It is known that silver telluride crystallizes in the monoclinic system with space group P21/c (β-Ag2Te) under ambient conditions1,2. In recent decades, β-Ag2Te has attracted significant interest as a promising candidate for thermoelectric material, infrared detection and magnetic field sensor3,4,5. Besides, β-Ag2Te was reported as a 3D topological insulator (TI), which acts as insulators in its bulk while has metallic Dirac fermions on its surface6,7,8. Considerable exotic quantum phenomena have been found in TIs such as Majorana fermions, magnetoelectric effect and quantum anomalous Hall effect9,10,11. On the other hand, pressure has been widely considered as an effective tool for turning crystalline structures and electronic band structures. For example, pressure-induced electronic topological transition (ETT) transforms Sb2Se3, BiTeI and As2Te3 from insulators into TIs12,13,14,15,16. In particular, pressure is critical to the formation of topological superconductors17,18,19,20,21. Moreover, it is obvious that the pressure-induced phase transition sequences for silver chalcogenides are very different22,23,24. For Ag2S22, it experiences a phase transition sequence: P21/n → P212121 → P21/n. For Ag2Se23, it undergoes structural changes: P212121 → Pnma → Cmcm. For Ag2Te24, Zhao et al. reported that an isostructural P21/c phase comes at 2.4 GPa and the Cmca phase emerges at 2.8 GPa, while the structure of the third high-pressure phase in Ag2Te is still unknown. Therefore, it is interesting to further investigate the high-pressure structural behaviors for Ag2Te. Besides, in order to meet the technological application of 3D TIs, a good bulk insulating character is necessary. However, so far, only Bi2Se3 exhibits an increase of the bulk resistivity under compression25,26,27. Therefore, it is important to explore the electrical transport property of β-Ag2Te by applying pressure, in order to find a better candidate for implementing devices with 3D TIs.

Here, we report an enhanced topological nature and determination of high-pressure crystal structures for Ag2Te by in-situ high-pressure resistivity measurements up to 28.4 GPa and room-temperature synchrotron angle-dispersive X-ray diffraction (ADXRD) measurements up to 33.0 GPa, using a diamond-anvil cell (DAC), in conjunction with first-principles calculations.

Results

With increasing pressure, the first and the second pressure-induced structural transitions of Ag2Te 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 P21/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 methodology28 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 P21/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 P21/c and Cmca phase rather than an isostructural P21/c phase24. 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 A2B compounds23, 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.

Table 1 Rietveld refinement results for 2.2 GPa.
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Table 2 Rietveld refinement results for 25.5 GPa.
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Figure 1
figure 1

Angle dispersive X-ray powder diffraction patterns of Ag2Te under high pressure at room temperature.

Arrow and asterisk represent new diffraction peaks.

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The schematic representation of the high-pressure phase transition sequence for Ag2Te is located in Supplementary Fig. S7. It is indicated that the structure of the P21/c phase is built up of stacking layers of edges-sharing [TeAg8] coordination polyhedron along a axis and the Cmca and Pnma phase structures can be presented with stacking layers of [TeAg9] coordination polyhedron sharing common faces. The detailed Ag-Te bond lengths of P21/c, Cmca and Pnma phase are located in Supplementary Table S2. It is obvious that Ag-Te bond lengths of Cmca phase all decreased under pressure. During the transition process from P21/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 P21/c phase monotonically decrease with increasing pressure. The linear compressibility of the different axes in the P21/c phase are κa = 0.0664(3) GPa−1, κb = 0.0230(7) GPa−1 and κc = 0.0314(3) GPa−1, respectively. It can be seen that 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—Bi2Te3, Bi2Se3 and Sb2Te325, the above abnormal changes may be ascribed to an ETT around 1.8 GPa.

Figure 2
figure 2

(a) Lattice parameters and (b) lattice constant ratios as a function of pressure for the P21/c phase. The solid lines are guide for the eyes. Errors given by the GSAS EXPGUI package are smaller than the marker sizes.

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The presence of active lone electron pairs (LEPs) can result in the asymmetry of coordination polyhedron12,29. Here, the variance of Ag-Te distances, K, is used to quantify the distortion of coordination polyhedron30. Based on the Ag-Te distances of P21/c phase in Supplementary Table S2, the pressure dependence of K in P21/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 orbital31 and the existence of the weaker interlayer interaction32. 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 κa = 0.0174(5) GPa−1, κb = 0.0144(4) GPa−1 and κc = 0.0336(6) GPa−1. This is unlike the previous result that a axe was reported more compressible than b and c axes24. As shown in Supplementary Fig. S9(c), the linear compressibility of the different axes in the Pnma phase are κa = 0.0136(6) GPa−1, κb = 0.0063(2) GPa−1 and κc = 0.0118(5) GPa−1.

Supplementary Fig. S10 shows the pressure-volume (P-V) relationships of the P21/c, Cmca and Pnma phase. These P-V data are fitted to the usual Birch-Murnaghan (BM equation of state (EOS)33.

where B0 is the bulk moduli and is the pressure derivative. The were fixed at 4 for all the phases. We obtain B0 of 66.48(7) GPa (V0 = 67.78(2) Å3) for the P21/c phase, B0 of 76.89(8) GPa (V0 = 65.84(0) Å3) for the Cmca phase and B0 of 99.03(0) GPa (V0 = 62.93(9) Å3) 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 P21/c phase, which suggests that the larger B0 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 P21/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 P21/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 Ag2Te 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 Ag2Te at room temperature. The electrical resistivity for Ag2Te 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 ETT34. Therefore, in order to shed light on the notable change in the P21/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 Ag2Te. However, Zhao et al. performed first-principles calculation on P21/c and Cmca phase in order to study the pressure-induced metallization.

Figure 3
figure 3

Resistivity as a function of pressure for Ag2Te at room temperature.

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As shown in Fig. 4(a,b), bulk Ag2Te 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, Ag2Te 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 Ag2Te 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 pressure26. On the other hand, it is found that the increasing interlayer spin-orbit coupling and the fluctuation of LEP activity35 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 transition36. Given this indirect-to-direct transformation of Ag2Te, the above assumption of a pressure-induced ETT appears reasonable25,37.

Figure 4
figure 4

Calculated band structures of Ag2Te at (a) ambient pressure, (b) 1.0 GPa and (c) 2.0 GPa, respectively. Total DOS and PDOS results of Ag2Te at (d) ambient pressure, (e) 1.0 GPa and (f) 2.0 GPa, respectively.

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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 Ag2Te 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/T38. 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 Ag2Te by applying pressure.

Figure 5
figure 5

(a) Temperature dependence of resistivity for Ag2Te. The inset shows resistivity vs temperature at 1.6, 1.8 and 4.1 GPa, respectively. (b) Pressure dependence of the carrier activation energy for Ag2Te.

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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 materials25. 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 impurities25. For Ag2Te 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 Ag2Te, it is verified that pressure is helpful for suppressing bulk conductivity and revealing the relative contribution of surface states conductivity25. So, a better topological nature of Ag2Te was obtained by compression. The electronic band structures of Ag2Te 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 expected26. (b) Due to indirect-to-direct band-gap transition, Ag2Te becomes a direct band-gap semiconductor after ETT, which is unique for 3D TIs, being a better candidate for infrared detection4,39. (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 Bi2Te3, Bi2Se3 and Sb2Te320,21,26.

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 properties25,32,40. For example, in previous report, the resistivity of Ag2−δTe decreased continuously as pressure increased to 1.0 GPa and showed a positive pressure coefficient beyond that pressure41. For purchased sample of Sb2Se312, the Raman study did not reproduce the pressure-induced ETT, but it can be observed in single crystal grown by Bridgeman method42. For Bi2Se3, different authors observed ETT and structural transition at pressures differing by 2–3 GPa18,19,26,27,43,44. In particular, for Bi2Te3, different hole concentration could give rise to the observations of pressure-induced superconductivity differing by 3–6 GPa20,33 and the pressure-induced ETT did not appear in n-type samples45.

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 polyhedron29. (b) By means of the changes of the lattice constant ratios, Raman frequencies and Raman linewidths, pressure-induced ETTs have been revealed in Bi2Te3, Bi2Se3 and Sb2Te3, which indicated both XRD measurements and Raman scattering measurements are sensitive methods to evidence the presences of ETTs in this family25. (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 TIs25,46,47. Thus, an improvement of thermoelectrical property can be expected in Ag2Te after ETT. (d) For both Bi2Se3 and Ag2Te, pressure-induced ETTs can affect the pressure coefficients of resistivity27. Based on the change in pressure coefficients of resistivity, we determine that the best topological nature of Ag2Te 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 density25. Since, for TIs family, the positive pressure coefficient of bulk band-gap is only found in Ag2Te, it is necessary to perform systematic studies on Ag2Te under compression, which may provide us an approach of enhancing bulk band-gap of 3D TIs. Thus, some suggestions are as follows: different stoichiometric Ag2±δTe, 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 Ag2Te upon pressure. Low-temperature electrical transport experiments are expected to discover topological superconductor states of Ag2Te.

Methods

Room-temperature angle-dispersive X-ray diffraction

Ag2Te 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 μm diameter hole drilled in the T-301 stainless steel gasket and chips of ruby were added as pressure calibrator49. 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 package50.

High-pressure resistivity measurements

Van der Pauw electrodes were integrated on one diamond anvil for in situ resistivity measurement under high pressure51. 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 methodology28. 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) code52 and the generalized gradient approximation (GGA)53 is implemented on a projector augmented wave (PAW) basis54,55. 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.

Additional Information

How to cite this article: Zhang, Y. et al. Electronic Topological Transition in Ag2Te at High-pressure. Sci. Rep. 5, 14681; doi: 10.1038/srep14681 (2015).