Antimony telluride (Sb₂Te₃) is a member of the (Bi, Sb)₂(Te, Se)₃ family with a narrow band gap. These layered chalcogenides are typical thermoelectric materials.^[1–3] Hence these materials and their alloys are widely studied. Compared with bulk Bi₂Te₃ alloy, the thin-film thermoelectric material demonstrates a significant enhancement in the figure of merit at 300 K.^[4] First-principle calculations show that a uniaxial pressure applied perpendicularly to the plane of the layered structure substantially improves the power factor of Sb₂Te₃.^[5] Calculations also show that under a uniaxial pressure of 1.5 GPa, multiple valence band maximal value occurs which may enhance thermoelectric properties.^[6] Owing to the fast speed, excellent endurance, and low-programming energy, Sb₂Te₃ is a promising candidate for phase change random access memories (PRAMs).^[7] Recently, chalcogenides (Sb₂Te₃, Bi₂Te₃, and Bi₂Se₃) have received attention again, because they are predicted to be three-dimensional (3D) topological insulators.^[8–10] The topological insulator is a new class of material, which features single Dirac cone at the Γ point.^[11]

Pressure can reduce interatomic distances and tune material properties, so high pressure study is helpful to understand properties of materials. Studies of these layered chalcogenides have shown that each of these chalcogenides presents a pressure-induced superconductivity.^[12,13] Under ambient conditions, Sb₂Te₃ has a rhombohedral structure (R3m, α-Sb₂Te₃, phase I).^[14] It is a long puzzle to determine the crystalline structures of Sb₂Te₃ at high pressures.^[15–17] Through the x-ray diffraction (XRD) experiments, Zhao et al.^[18] reported that at about 9.3 GPa, Sb₂Te₃ started to transform from the rhombohedral structure to a monoclinic C2/m, and the transition to the monoclinic C2/m structure was completed at 12.3 GPa. At about 15.1 GPa, another disordered monoclinic C2/m structure emerged and this disordered C2/m structure was completely formed at 18.9 GPa. Then, it transformed to a disordered body-centered cubic Im3m structure at about 19.8 GPa and this transformation was completed at above 29.7 GPa. Thus, Sb₂Te₃ underwent a sequence of phase transitions as follows: rhombohedral R3m structure → (9.3 GPa) monoclinic C2/m structure → (15.1 GPa) disordered monoclinic C2/m structure → (19.8 GPa) disordered body-centered cubic Im3m structure. In the following mentioned experiments, we just focus on the pressure under which the new phase emerges, but will not mention the pressure ranges of coexistence at all.

Using XRD experimental technique, Souza et al.^[19] observed two high pressure phases at pressures of 9.8 GPa and 15.2 GPa, respectively. They determined that the first high pressure phase was of a monoclinic C2/m structure and the second was of an ordered C2/c structure. Recently, Ma et al.^[20] also explored the high pressure behaviors of Sb₂Te₃ at pressures of up to 52.7 GPa through angle-dispersive synchrotron x-ray powder diffraction (XRPD) technique in a diamond anvil cell and their experimental results showed that the phase (R3m, α-Sb₂Te₃) transformed into phase II (monoclinic sevenfold C2/m, β-Sb₂Te₃) and phase III (monoclinic eightfold C2/c, γ-Sb₂Te₃) around 8.0 GPa and 13.2 GPa, respectively, and at above 21.6 GPa, a disordered body-centered cubic Im3m structure (phase IV, δ-Sb₂Te₃) emerged. This phase sequence is consistent with the transition sequence of Bi₂Te₃.^[21]

In our present work, using the plane-wave pseudopotential density functional theory (DFT) method as implemented in the Cambridge Serial Total Energy Package (CASTEP) code,^[22,23] we investigate the phase transition and elastic properties of Sb₂Te₃ under pressure. Since the calculations of the disordered bcc phase are not possible in the CASTEP code, we just discuss the phases I, II, and III in our following calculations. The remaining parts of this paper are organized as follows. In Section 2, the computation details are presented. The results and discussion are shown in Section 3. Then electronic properties are discussed in Section 4. Finally, a summary of our results is given in Section 5.

Equilibrium properties, such as bulk moduli, phonon frequencies and magnetisms are sensitive to lattice constants. Generally speaking, the lattice constants predicted from PBESOL^[24,25] exchange–correlation functional were better than those predicted from the local spin density approximation (LSDA), the Perdew–Burke–Ernzerh (PBE) version of the generalized gradient approximation (GGA) or the Tao–Perdew–Staroverov–Scuseria (TPSS) meta-GGA. Thus the PBESOL was employed for describing the exchange–correlation energy of electrons. The ultrasoft “on the fly” pseudopotential^[26] was chosen for the interaction of the electrons with the ion cores, and pseudo atomic calculations were performed for Sb-5s²5p³ and Te-5s²5p⁴. The electronic wave functions were expanded in a plane wave basis set with an energy cut-off of 260 eV. For the Brillouin-zone sampling, we used the Monkhorst–Pack meshs^[27] 8×8×8, 8×8×3 and 3×3×2 for phases I, II, and III, respectively. In the geometry optimization, criteria of convergence were set to be 5×10⁻⁶ eV/atom for energy, 0.01 eV/Å for force, 5×10⁻⁴ Å for ionic displacement, and 0.02 GPa for stress. In calculations of elastic properties, criteria of convergence were set to be 1×10⁻⁶ eV/atom for energy, 0.002 eV/Å for the maximum force, 1×10⁻⁴ for the maximum ionic displacement, and 0.003 GPa for the maximum strain amplitude. These parameters are carefully tested and sufficient to lead to a well converged total energy.

The partial densities of states (PDOSs) of three phases, i.e., phase I at 0 GPa, phase II at 10 GPa and phase III at 15 GPa are shown in Fig. 4. For phase I (see Fig. 4(a)), the lower valence band (−14 eV–10.5 eV) is contributed from Sb-5s, Sb-5p, Te₁-5s, and Te₂-5s states. The middle valence band (−10 eV ∼ −7 eV) originates from Sb-5s, Te₁-5s, Te₂-5s, Te₁-5p, and Te₂-5p states in which the Sb-5s states are dominant. The upper valence band (−6 eV ∼ 0 eV) is mainly comprised of the contributions from Sb-5s, Sb-5p, Te₁-5p, and Te₂-5p states, and it is dominated by Sb-5p, Te₁-5p, and Te₂-5p states. In the conduction band, the Sb-5p, Te₁-5p, and Te₂-5p states play the dominant role in a range from 0 eV to 5 eV and the range from 5 eV to 9 eV consists of the constructions from Sb-5s, Te₁-5s, and Te₂-5s states. According to the analysis above, in the whole valence band, we discover that Sb-5s states hybridize with Te-5s states in an energy range from −14 eV to −7 eV and Sb-5p states strongly hybridize with Te-5p states from −6 eV to 0 eV. These hybridizations imply the existence of covalent bonding in α-Sb₂Te₃. For phase II (Fig. 4(b)), in the valence band, the energy range from −15 eV to −7 eV is mainly composed of the contributions from Sb₁-5s, Sb₂-5s, Te₁-5s, Te₂-5s, and Te₃-5s states. The Sb₁-5p, Sb₂-5p, Te₁-5p, Te₂-5p, and Te₃-5p states play a dominant role in an energy range from −7 eV to 5 eV. For phase III (Fig. 4(c)), Sb-5s, Te₁-5s, and Te₂-5s states contribute to the energy range from −15.5 eV to −7.5 eV. The energy range from −7 eV to 5 eV is dominated by Sb-5p, Te₁-5p, and Te₂-5p states. From the analysis, we can notice that the hybridization between Sb-5s and Te-5s states and hybridization between Sb-5p and Te-5p states also exist in phases II and phase III. These hybridizations also indicate that there exist the covalent bondings in β-Sb₂Te₃ and γ-Sb₂Te₃. It is found that energy range of conduction band of each of phases II and III is smaller than that of phase I, while energy ranges of valence band of phases II and III are slightly larger than that of phase I. Furthermore, the pressure-induced metallization is a well-known phenomenon in semiconductor. From the PDOSs of high pressure phases, we can infer that they exhibit a metallic behavior, which accords with the conclusion of other paper.^[20]

Fig. 4.

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	Fig. 4. Calculated PDOS versus energy for (a) phase I at 0 GPa, (b) phase II at 10 GPa, and (c) phase III at 15 GPa.

In this work, we study the phase transitions, elastic and electronic properties of α-Sb₂Te₃ (R3m), β-Sb₂Te₃ (C2/m) and γ-Sb₂Te₃ (C2/c), by using first principle calculations based on the density functional theory. The calculated lattice constants of three phases are in agreement with their experimental values. The enthalpies of all the structures are calculated under a pressure range of 0 GPa–28 GPa. Solving the cross-point of enthalpy, we obtain the phase transition pressures to be 9.4 GPa for phases I to II and 14.1 GPa for phase II to phase III respectively. These results are consistent with experimental data. Elastic constants C_ij, bulk modulus B, shear modulus G of the three phases are calculated and the obtained values of B/G indicate that phase I and III are brittle, while the phase II is ductile. Young’s modulus E, Poisson’s ratio σ, shear acoustic velocity V_S, longitudinal acoustic velocity V_L, average acoustic velocity V_m, and Debye temperature Θ are also studied and all these quantities increase from phase I to phase III, except the Poisson’s ratio σ. The universal anisotropy index A^u suggests the order of degree of elastic anisotropy is phase II (3.3) > phase I (2.9) > phase III (1.2). In the end, the partial densities of states are studied, suggesting that there are some covalent features in the three phases and high pressure phases show metallic behaviors.