Pressure induced Ag 2 Te polymorphs in conjunction with topological non trivial to metal transition

Silver telluride (Ag2Te) is well known as superionic conductor and topological insulator with polymorphs. Pressure induced three phase transitions in Ag2Te have been reported in previous. Here, we experimentally identified high pressure phase above 13 GPa of Ag2Te by using high pressure synchrotron x ray diffraction method in combination with evolutionary crystal structure prediction, showing it crystallizes into a monoclinic structure of space group C2/m with lattice parameters a = 6.081A, b = 5.744A, c = 6.797 A, β = 105.53°. The electronic properties measurements of Ag2Te reveal that the topologically non-trivial semiconducting phase I and semimetallic phase II previously predicated by theory transformed into bulk metals for high pressure phases in consistent with the first principles calculations.


I. INTRODUCTION
Ag 2 Te, which occurs naturally as the mineral hessite, has attracted considerable interest in recent years.2][3][4][5][6][7][8][9] High temperature fcc (α) and bcc (γ) -structured phases, characterized by the fast-moving Ag + ions, can be used as superionic conductor. 24][5] The β-Ag 2 Te has a high electron mobility 6 and low thermal conductivity 7 and thus is very sensitive to external effects, such as pressure.1][12][13] In particular, a quantum scenario was proposed very recently based on the assumption of gapless linear energy spectrum, in which β-Ag 2 Te was confirmed to be a new kind of possible topological insulator with a highly anisotropic Dirac cone. 13,14Remarkably, all these unique characteristics mentioned above make Ag 2 Te very promising for practical applications as a multi-functional compound.
Pressure, just as temperature and chemical composition, belongs to one of the three fundamental thermodynamic variables.9][20][21] Very recently, high-pressure x-ray diffraction (XRD) experiments combined with first-principle calculations demonstrated that β-Ag 2 Te (phase I) transit into phase II, III and IV at 2.4 GPa, 2.8 GPa and 12.8 GPa, respectively, and phase III has been solved to be an orthorhombic structure with the centrosymmetric space group Cmca. 21However, the electrical and crystal structure of phase IV have not been determined and the potential effect of the structural phase transitions on the electrical transport properties of Ag 2 Te is still unknown.
To provide insights into the pressure behavior of topological insulator Ag 2 Te, studies of electrical transport properties based on electrical conductivity measurements under high pressures and low temperatures were conducted.We have also performed crystal structure analysis in combination with theoretical calculations on Ag 2 Te to explore both crystal & electronic structural evolutions as a function of pressure.Our results reveal that β-Ag 2 Te, which exhibits linear MR behavior due to its topologically non-trivial nature in phase I and phase II, will show distinct electrical behaviors with quadratic MR responses under higher pressures.3][24] The electrical and crystal structures of phase IV are also identified in combination with theoretical calculation.

II. EXPERIMENTAL DETAILS
High-purity stoichiometric Ag 2 Te (>99.9%) were obtained from Sigma-Aldrich Company.We used diamond anvil cell in combination with Maglab system to investigate the electronic transport properties under pressure at low temperatures.Sample was loaded into a hole with 200 µm diameter in a T301 stainless-steel gasket that is preindented from the thickness of 300 µm to 60 µm.The culet of diamond is 500 µm in diameter.The size of the sample was about 100 µm*100 µm*20 µm.Cubic boron nitride (cBN) was used as insulating layer between the gasket and the electrodes, while the hexagonal boron nitride (hBN) was used as the pressure transmitting medium.The electrode leads were 18-µm-diameter gold wires.Electrical resistance measurements were performed by a standard four-probe technique.
The in situ high-pressure angle-dispersive X-ray diffraction (ADXRD) method is utilized for the structural studies of Ag 2 Te powder samples.The experiments are performed at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory with λ = 0.4134 Å using symmetric diamond anvil cells with a pair of 300 µm cullet diamonds.Silicone oil was used as the pressure transmitting medium to provide a fine quasi-hydrostatic pressure environment.The diffraction patterns are collected using a Mar345 image-plate detector.The two-dimensional diffraction images were studied using the FIT2D software.Data analysis of the high pressure (HP) synchrotron x-ray patterns was performed using the GSAS-EXPGUI package. 25In both types of experiments pressure was determined by the ruby fluorescence method. 26o find the structure of the new phase, we used the evolutionary crystal structure prediction method USPEX, 27,28 which has been successfully used in many previous works, in particular finding new chemistry under pressure. 27,29For reviews of different crystal structure prediction methods and their comparison, see Ref. 30, USPEX derives its particularly strong efficiency and reliability from a special symmetry-based random structure generation procedure 28 and the use of smart variation operators 28 and fingerprint theory. 31Structure prediction calculations were performed at 15 GPa for systems with 6, 9, 12 and 18 atoms in the unit cell (2, 3, 4 and 6 formula units, respectively).Each generation consisted of 20-40 structures, depending on system size.The initial generation and 20% of the structures of all subsequent generations were produced randomly, with each structure generated within one of 230 space groups.All structures were relaxed; structure relaxations and enthalpy calculations were done using the VASP code 32 at the level of generalized gradient approximation 33 in conjunction with the all-electron PAW method. 34The PAW potentials used had [Kr] core (2.4 a.u.radius) for Ag atoms and [Pd] core (radius 2.3 a.u.) for Te atoms.Brillouin zone integration was done with Γ-centered uniform meshes with resolution 2πx0.09Å −1 and Methfessel-Paxton electronic smearing with σ = 0.1 eV, and wave functions were expanded in plane waves with kinetic energy cutoff of 350 eV.After relaxation with the above settings, the total energy was recalculated using a much more stringent k-mesh of resolution 2πx0.05Å −1 .Self-consistency threshold was 10 −4 eV/cell, and relaxation was done until the enthalpy changed by less than 10 −3 eV/cell.These settings ensured excellent precision and efficiency of the calculations.After all structures in a generation are relaxed and ranked by enthalpy, the lowest-enthalpy 60% of the structures are used for producing the next generation of structures using heredity (60% of the structures), permutation (10%), soft mutation (10%), and symmetric random generator (20%), and in addition 3-5 different lowest-enthalpy structures are allowed to survive into the next generation.The calculations of accurate electronic structures are performed using the full-potential linearized augmented plane-wave method, 35 implemented in the package WIEN2K. 36The exchangecorrelation effect was treated with the Perdew, Burke, and Ernzerhof parameterized generalizedgradient approximation. 33The converged ground states are obtained using the k-mesh of resolution 2π×0.02Å −1 and K max R MT = 9.0, where R MT represents the smallest muffin-tin radius and K max is the maximum size of reciprocal-lattice vectors.The muffin-tin radiuses for both Ag and Te are set to 2.5 Bohr.Spin-orbit coupling was included by a second-variation procedure, 35 where states up to 9 Ry above Fermi level were included in the basis expansion.The effect of pressure on the electronic properties can be more clearly seen in Fig. 1(b) where the resistance at given temperature is plotted as function of pressure.Upon compression, the resistance decreases with increasing pressure below 1.6 GPa.Then it shows an abrupt increase at around 2 GPa, followed by a sharp decrease with pressure from 2.2 GPa to 3 GPa.The p-type character at ambient pressure also changes to n-type character above 2.5GPa (as shown in Fig. S1). 38The abnormal increase of resistance probably originates from a pressure-induced electronic topological transition (ETT).The ETT occurs when an extremum of the electronic-band, which is associated to a Van Hove singularity in the electronic density of states (EDOS), crosses the Fermi energy level leading to a strong redistribution of the EDOS near the Fermi energy level. 37The redistribution of the EDOS leads to a second-order isostructural phase transition, which is closely related to its hole concentration.Following the ETT, a phase transition from phase II to phase III occurs at about 3 GPa, corresponding to the sharp decrease of resistance.After that, the resistance decreases at a much slower rate as the pressure approaches 12 GPa.When pressure is higher than 12.8 GPa, the resistance passes through a minimum and then increases up to the maximal experimental pressure.It is in accordance with the pressure point where structural phase transition from phase III to phase IV was observed in previous paper. 21The distinct pressure dependence of resistance is clearly related to these four phases since the change of electrical and crystal structures modifies the Fermi surface, which is tightly related to the electrical transport properties of Ag 2 Te.

III. RESULTS AND DISCUSSION
The effect of pressure on the electronic structure can also be reflected from the magnetoresistance (MR).Fig. 2 exhibits the magnetic-field dependence of the magnetoresistance ∆R(B)/R(0) = [R(B) − R(0)]/R(0) at 2 K at different pressures.At 1.3 GPa, ∆R(B)/R(0) increases with increasing H and there is no evidence of saturation up to at least 6T.The value of ∆R(6T)/R(0) is 5% and the critical field where MR crosses over from a quadratic to a linear dependence on H is about 1T.As the pressure increases to 2.5 GPa, the linear MR behavior is suppressed continuously and shows more quadratic character.Further increasing pressure above 3.3 GPa results in a completely quadratic MR response.The nonsaturating linear MR behaviors were previously observed in Ag 2 Te at ambient pressure, 8,9 which may have large contribution from the topological nature. 13As completely quadratic MR corresponds to the bulk metallic phase III, it is reasonable FIG. 2. Normalized magnetoresistance ∆R(B)/R(0) = [R(B) − R(0)]/R(0) at T=2.0K under transverse magnetic field at a series of pressures.The linear MR will be gradually substituted by quadratic MR as pressure rises.to infer that the electronic structure of Ag 2 Te at high pressures no longer keeps its topological character.
To complement our studies of properties of Ag 2 Te under high pressure, we further performed in situ high pressure synchrotron X-ray powder diffraction experiments at room temperature with pressure up to 30 GPa.Selected diffraction patterns of Ag 2 Te are plotted in Fig. 3.At 0.2 GPa, all the diffraction peaks can be indexed to the structure of ambient β-Ag 2 Te with space group P2 1 /c.At about 2.2 GPa, Ag 2 Te starts the structural phase transformation as some peaks vanished and new peaks appeared (as shown in Fig. S2), and the transition completes at about 3.4GPa. 38Note that the transformation from phase III to phase IV completes at 17 GPa.No new peak appears for pressure up to 31.2 GPa (as shown in Fig. S3). 38alculations with the USPEX method reveal the lowest-enthalpy structure found at 16 GPa has space group C2/m and theoretical cell parameters a = 6.08123Å, b = 5.74370 Å, c = 6.79746Å, β = 105.53• with atomic positions Ag (0.58369, 0.5, 0.30281), Ag (0.25, 0.75 0.0) and Te (0.61390, 0.0, 0.31017).The structure is shown in Fig. 4 and can be described as a compact layered monoclinic structure with triple Te(Ag2)-Ag1-Te(Ag2) layers similar to those in phase I, II and III.From phase III to phase IV, pressure tends to increase the coordination number for Ag1 from five to nine, in which each Ag atom among its 9 nearest neighbors has 5 Te and 4 Ag atoms at distances in the range of 2.7-3.2Å.The X-ray diffraction patterns of Ag 2 Te at high pressure are analyzed with Rietveld refinements by using the GSAS program package.A typical refinement result at 17 GPa is shown in Fig. 3 in which the fitted residual Rp and Rpw were 2.72% and 2.05%, respectively.Table I lists the theoretical and experimental cell parameters based on the refinement for comparison.The theoretical profiles fit the experimental data in good way, which enabled us to determine the crystal structure of phase IV unambiguously.
The observed abnormal behaviors in the resistance and MR suggest a pronounced modification of the electronic structure of Ag 2 Te under pressure.From Fig. 1 and Fig. 2, we find that phase I is a narrow-gap semiconductor which reveals linear MR behavior.The abrupt increase in the resistance as well as mixed quadratic and linear MR response between 2 to 3 GPa is consistent with the pressure range of the ETT in Ag 2 Te.Based on recent theoretical calculations of the electronic structure, 21 isostructural phase II maintains its topological nontrivial surface state while the bulk changes to semimetal.That is, the bulk metallic properties dominate the surface properties, resulting in some degree of quadratic character in the MR behavior.After structural phase transition, phases III behaves like metals with quadratic MR response.Note that the resistance of Ag 2 Te at phase III decreases smoothly with increasing pressure, and after passing through a minimum at around 12 GPa, starts to increase in phase IV after the third phase transition.An analysis of the densities of states suggests that phase III is a bulk metal. 21To further clarify the nature of metallic behavior of phase IV, we studied the electronic structures using first-principles calculations based on density functional theory and the generalized gradient approximation with spin orbital coupling(SOC).The band structure of phase IV at experimentally refined crystal structure is plotted in Fig. 5, in which one can clearly see the metallic feature with complex multibands crossing the Fermi level.The metallicity of phase IV identified from the band structure is in good agreement with our experimental measurefments.Although this system is a metallic phase, it has local band gap everywhere in entire Brillouin zone.Therefore, the Z 2 topological invariants can be well defined.The calculated Z 2 invariants (0;000) indicate that this high-pressure phase is a metal.
In order to have a more intuitive understanding of the structural and electronic evolution of Ag 2 Te under pressure, we plot in Fig. 6 the pressure-temperature phase diagram based on the results mentioned above.Phase I and phase II which have topological nontrivial surface states can only stabilize in a narrow pressure range.At pressure above 3 GPa, phase III and phase IV appears in sequence, converting Ag 2 Te from topological insulator into topologically trivial metal.
In summary, the high pressure structure of Ag 2 Te at phase IV was analyzed based on experimental results in combination with theoretical optimization to be a monoclinic layered structure (space group C2/m).Electrical conductivity measurements show that semimetal phase II preserve its topological nontrivial nature with mixed quadratic and linear MR response, while both the phase III and IV are bulk metals with non-saturating quadratic MR behavior.

Fig. 1 ( 4 Zhu
Fig.1(a)shows an overview of resistance in longitudinal scale as a function of temperature at a series of pressure points.At pressures close to ambient, the resistance gradually increases at first by decreasing temperature, which is a typical behavior for semiconductors.The resistance reaches

FIG. 4 . 6 Zhu
FIG. 4. Schematic view of the crystalline structure of Ag 2 Te at phase IV.

FIG. 5 .
FIG. 5. Electronic band structure of Ag 2 Te at phase IV based on experimental measurements of the crystal lattice.A metallic state for phase IV is obtained.

TABLE I .
Crystal structural data of Ag 2 Te II at 17.0 GPa derived from Rietveld refinements in Figure3.The theoretical lattice parameters and internal atomic sites of Ag 2 Te II at 16.0 GPa are listed in parenthesis.