Pressure-induced superconductivity in SnSb₂Te₄

Sample preparation and characterization

The coarse-grained single crystals of SnSb₂Te₄ were prepared by a self-flux synthetic route. Powders of the elements Sn, Sb, and Te with a purity better than 99.99% were used as purchased (Aladdin Company, China). They were mixed together according to the expected atomic ratio (Sn:Sb:Te = 1:2:4). The initial reactants were ground vigorously in an agate mortar to turn them into a homogenous mixture. The mixture was then transferred into a quartz ampule. The ample was evacuated and sealed to ensure airtightness. The temperature of the ampule was raised to 950 °C at a heating rate of 40 °C per hour. The high temperature transformed the reactants into a melting flux and induced reactions among them. Afterward, the temperature of the ampule was lowered to 500 °C at a rate of 20 °C per hour. The products were annealed at this temperature for four days. At last, the power supply was turned off, and the temperature of the ampule was lowered to room temperature in a natural cooling mode. In this way, single crystals of SnSb₂Te₄, with a black color, were successfully prepared and finely powdered in an agate mortar for convenience in high pressure studies. The morphologies of the obtained powders were characterized using SEM images taken on a Hitachi S4800 microscope. The elemental compositions were characterized using an energy dispersive X-ray spectrometer (EDX).

ADXRD studies at high pressures

In situ high pressure angle dispersive XRD (ADXRD) experiments were carried out using a symmetric diamond anvil cell (DAC). The culets of the two diamond anvils were about 300 µm in diameter. The gasket was made of T301 stainless steel. A hole about 50 µm in diameter was drilled at the center of the gasket, serving as the sample chamber. The prepared powders of SnSb₂Te₄ were loaded into the sample chamber together with a small chip of ruby, which was used as the pressure indicator^[27]. The mixture of methanol and ethanol in a volume ratio of 4:1 was used as the pressure transmitting medium. In situ high pressure ADXRD experiments were performed at the high pressure station on the 4W2 beam line of Beijing Synchrotron Radiation Facility (BSRF). The wavelength of the incident monochromatic synchrotron X-ray was 0.6199 Å. The XRD data were recorded using a MAR image plate. The Dioptas package was employed to process the raw XRD data^[28]. The full profile indexing and refinements of the diffraction patterns were carried out using the GSAS+EXPGUI package, employing the Le Bail method^[29].

Electrical measurements at high pressures and low temperatures

The electrical transport characteristics of SnSb₂Te₄ at high pressures and low temperatures (HPLT) were investigated using a symmetric DAC with two 300 µm culet diamond anvils. In order to prevent short circuits between the electrode leads and the gasket, fine powders of Al₂O₃ were employed to cover the T301 stainless steel gasket on one side to form a layered composite gasket. The gasket was initially 250 µm in thickness and pre-indented to about 30 µm. A hole with a diameter of 260 µm was drilled at the center of the indented region. Then, fine powders of Al₂O₃ were filled and compressed in the hole. Finally, a hole with a diameter of 150 µm was drilled at the center of compact Al₂O₃ to serve as the sample chamber, and the sample powders of SnSb₂Te₄ were loaded into it. To ensure reliable contact between the electrodes and the sample powders, pressure transmitting medium was avoided in electrical measurements. The pressure was calibrated using either the ruby fluorescence R1 line^[27,30,31] or the high frequency edge of the Raman scattering peak of diamond^[32] (at low temperatures). Pt wires with a diameter of 4 µm were employed as the electrodes. The electrical resistance of the sample was measured using the traditional four-probe method. The electric voltages and currents involved were measured using a Keithley 2182A nanovoltmeter and 6221 AC and DC sources, respectively. The low temperature conditions were generated and maintained using an integrated low temperature system (Janis PTSHI-950-LT). The sample was compressed under 41 GPa at increments of approximately 2 GPa and cooled down to 5.2 K from the ambient temperature. After each increment, a temperature cycle was performed. The rate of temperature slowly decreased to ensure temperature equilibrium.

Theoretical simulation

Ab initio energetic and electronic calculations of SnSb₂Te₄ were performed based on the framework of DFT as implemented in the Vienna ab initio simulation package (VASP)^[33]. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional^[34] was adopted to describe the exchange-correlation energies. The electron-ion interaction was described using the projector augmented wave (PAW) method^[35], considering 5s²5p², 5s²5p³, and 5s²5p⁴ as valence electrons for Sn, Sb, and Te atoms. The cutoff energy of the plane waves was set at 900 eV. The fine Monkhorst-Pack^[36]k meshes with a spacing of 2π × 0.18 Å^-1 were adopted in order that the calculated enthalpy were well converged to values with an accuracy higher than 1 meV/atom. The spin-orbit coupling effect was considered in the calculations of the electronic band structures.

Physical characterization under ambient pressure

The crystal structure of SnSb₂Te₄ is shown in Figure 1A. Under ambient conditions, the crystal structure of SnSb₂Te₄ belongs to the trigonal system with the R-3m space group (phase I). In the structure, rocksalt-type building blocks comprising septuple layers (SLs) of alternating cations and anions are stacked along the crystallographic c axis. The SLs, with the ideal sequence of Te₁-Sb-Te₂-Sn-Te₂-Sb-Te₁, are held together through the van der Waals gaps between the hexagonal Te layers terminating the blocks. The hexagonal unit cell includes three SLs. Based on the Le Bail refinement of the XRD patterns of SnSb₂Te₄ powders [Figure 1B] using GSAS, the unit cell parameters are determined: a = 4.301 Å and c = 41.598 Å. The results are consistent with those reported previously^[37]. The typical scanning electron microscope (SEM) image of the as-prepared SnSb₂Te₄ sample is shown in Figure 1C. It shows that the prepared sample consists mainly of flakes with irregular shapes due to vigorous grinding treatment. However, all the flakes show clearly flat basal planes since they were actually broken single crystals. The size of the flakes ranges from 1 to 10 μm. The chemical composition of the sample was measured by energy-dispersive X-ray spectroscopy (EDS). Figure 1D demonstrates that the sample comprises mainly Sn, Sb, and Te elements. In a wide spectrum range (0-10 keV), no signal from any other element is detectable. Through quantitative analysis based on the EDX spectra, the atomic ratio of Sn:Sb:Te is estimated to be 1:2:4, in good agreement with the proposed chemical formula.

Figure 1. (A) The crystal structure of SnSb₂Te₄. The square frame shows a single SL building block. Blue, green, and magenta balls stand for Sn, Sb, and Te atoms. (B) The typical XRD patterns of SnSb₂Te₄ powders at ambient pressure. (C) The typical SEM image of the as-prepared SnSb₂Te₄ powders. (D) The typical EDX spectra of the as-prepared SnSb₂Te₄ powders.

Pressure-induced structural transformations

In the ADXRD studies, it was observed that SnSb₂Te₄ experienced three sequential structural phase transitions under compression at 0-45.6 GPa [Figure 2A]. As pressure increased to approximately 6.3 GPa, the emergence of new diffractions (marked with solid circles) indicated that the initial trigonal structure (phase I) lost stability, and a new phase (denoted as phase II) appeared. Phase II was fully established at > 12.9 GPa. It was noteworthy that phase I persisted and coexisted with phase II up to approximately 8.9 GPa. Previous studies on SnSb₂Te₄^[20] under high pressures demonstrated the pressure-induced decomposition at > 7 GPa. However, our experimental studies did not observe any signs of decomposition [Supplementary Figures 1-3]. To determine the structure of phase II, the pressure-induced phase transition sequences of the binary VA-VIA compound counterparts of SnSb₂Te₄, such as Bi₂Te₃^[38,39], Bi₂Se₃^[40], Sb₂Te₃^[41], Sb₂Se₃^[42], and Sb₂S₃^[17,43], and the related ternary ones, such as Bi₂Te₂Se^[44] and SnBi₂Te₄^[15], were considered. Therefore, phase II was assigned to a C2/m space group. The assignment could be validated based on the Le Bail refinement of the ADXRD patterns [Figure 3A]. The reflections from phase II can be indexed to the C2/m structure, yielding the lattice parameters summarized in Table 1. As the pressure further increased to 15.5 GPa, additional diffraction peaks appeared in the ADXRD patterns [marked with solid diamonds in Figure 2A, indicating the emergence of another new phase (phase III). Phase III remained stable at 15.5-40.2 GPa. Under the stable pressure range, phase III coexisted with phase II and/or phase IV. Owing to the complicacy of the ADXRD profiles, it becomes difficult to determine the exact crystal structure and lattice parameters of phase III. However, similar to the assignment of phase II, phase III might be tentatively assigned to a C2/c structure [Figure 3B]. With further increase of the pressure to 17.2 GPa, new diffraction peaks started to emerge, which were marked with black arrows in Figure 2A. They indicated the onset of the third phase transformation into phase IV. Phase IV at high pressures can be indexed to the body-centered cubic structure (space group No.229, Im-3m) with the unit cell parameter of a = 3.459 Å. Phase IV remained stable up to 45.6 GPa, the highest pressure achieved herein. Le Bail fitting for the XRD patterns at various pressures was shown in Figure 3A-D.

Figure 2. The structural evolution of SnSb₂Te₄ at high pressures. (A) The typical ADXRD patterns of SnSb₂Te₄ acquired at various high pressures and room temperature. The solid circles, diamonds, and arrows are used to indicate the emerging diffractions of phases II, III, and IV. (B) The pressure-dependent evolution of the d-spacings of SnSb₂Te₄. The pressure ranges in which the structural phases exist are labeled with vertical dash lines. Across the phase transition pressures, the slopes of the variation curves of the d-spacings change discontinuously.

Figure 3. The full profile diffraction patterns of SnSb₂Te₄ at (A) 8.9, (B) 15.5, (C) 3.1 and (D) 44.7 GPa. The solid lines in red represent the fitting curves of the diffraction patterns of the involved structures via Le Bail refinements, and open circles represent the experimental data points. The solid lines in black at the bottom represent the residual deviations between the fitted and the observed intensities. The vertical bars indicate the theoretical peak positions of the involved structural phases. The diffraction patterns in (A) comprise a mixture of phases I and II. Those in (B) comprise a mixture of phases II and III. (E) The pressure dependence of the lattice parameters for phase I. The lattice parameters are indicated by squares, solid circles, and hollow circles, corresponding to the data reported by Sans et al.^[20] and those obtained experimentally and theoretically in the present study. The inset shows the pressure dependence of the axial ratio c/a.

In the bcc (Im-3m) structure, it was demanded by symmetry that only one inequivalent atomic position at the 2a Wyckoff site was allowed. As a result, in phase IV of SnSb₂Te₄, the distribution of Sn, Sb, and Te atoms was disordered, and they had to share the bcc lattice sites in a random manner. Hence, an Sn-Sb-Te substitutional solid solution is formed. The similar phenomena have also been observed in the high pressure-induced substitutional solid solution phases in Bi₂Te₃, Sb₂Te₃, and Sb₂Se₃. The formation of the high pressure substitutional solid solutions can be roughly explained in terms of atomic size and electronegativity. As pressure was gradually increased, these parameters for different atoms tended to become almost homogenous. Thus, it turned out to be possible for them to form substitutional solid solutions at high pressures. Moreover, the pressure-dependent variation trends of the lattice d-spacings [Figure 2B] and the volume [Supplementary Figure 4] indicated additional signs of the phase transitions. Thus, based on the aforementioned results and discussion, for SnSb₂Te₄, the pressure-induced structural phase transition sequence might be R-3m → C2/m →C2/c → disordered Im-3m.

Several factors may contribute to the broadening of the diffraction peaks in high pressure XRD patterns. First, the non-hydrostatic stress in the samples may lead to systematic broadening and weakening of the diffraction peaks with increasing pressure. Second, amorphization, if it occurs, may lead to diffuse diffractions with large width and low intensity. In the third place, the overlapping of the diffraction peaks of coexisting phases may exhibit broad convolutional profiles when they have similar d-spacings. In this work, coexistence of phases II, III, and IV may be the major origin of the broadening of the diffraction peaks around 15-17 GPa. The occurrence of amorphization was hardly possible since the diffraction peaks in the low-angle range remained sharp and strong.

Pressure-induced electron topological transition

The pressure dependences of the experimental and theoretical lattice parameters and the axial ratio c/a of the initial phase are illustrated in Figure 3E. A minimum can be observed in the variation curve of c/a at approximately 3 GPa. Generally, it suggests the occurrence of the electron topological transition (ETT) near this pressure. These experimental results agree well with our theoretical calculations. The abnormal variation in the c/a ratio with pressure is considered as a good indicator of ETT. It is caused by the anomalous compression behavior of the a axis under high pressures, which results in a profound change in compressibility during ETT^[41]. The topological transition of electrons related to electrical transportation in SnSb₂Te₄ can be visualized based on the first-principles calculations of the electron energy bands [Figure 4]. Under ambient conditions, the minimum conduction band (MCB) and maximum valence band (MVB) appear at the high symmetric point (A) of the Brillouin zone (BZ). The calculation results of the density of states (DOS) indicate that Te mainly contributes to the MVB, and Sn contributes to the MCB. In agreement with previous reports^[22], SnSb₂Te₄ is a direct band gap semiconductor. However, the narrow band gap of 0.02 eV indicates that SnSb₂Te₄ may behave as a metal at room temperature owing to self-doping effects.

Figure 4. Electronic band structures of SnSb₂Te₄ at (A) 0.1, (B) 2.0, (C) 4.0, and (D) 6.0 GPa in the presence of spin–orbit coupling.

Under compression, the repulsion between the electron states of Te and Sn considerably increases with pressure. As a result, the positions of the MCB and MVB change substantially. SnSb₂Te₄ becomes an indirect band gap semiconductor. At 2.0 GPa, the MVB moves to a high symmetric point along the Γ-M direction in the BZ, with the complex contributions of Sn, Sb, and Te. Along the Γ-M direction near the Γ point, at least three dispersive branches compete for the MCB. The indirect band gap decreases with an increase in pressure. ETT occurs when an extreme of the electronic band structure, which is associated with the Van Hove singularity in the DOS, exceeds the Fermi energy (EF) and leads to a strong redistribution of the EDOS near the EF^[43]. In one of the previous studies that reported the analysis of SnBi₂Te₄ under high pressures, a discontinuous change in the c/a ratio under pressure was found to be related to the inflection point of electrical resistance at 2 GPa, which implies the occurrence of ETT in phase I^[15]. Moreover, ETT existed based on the phonon spectrum measurements observed in the parent binary compound, i.e., Sb₂Te₃^[45], and the compounds of the A₂B₃ chalcogenide series, e.g., Bi₂Se₃, Sb₂S₃, and Bi₂Te₃^[40,43,46].

Pressure-induced superconductivity

The temperature dependence of the electrical resistance of SnSb₂Te₄ was obtained at 12.3-41 GPa[Figure 5A]. At < 12.3 GPa, the conducting behavior is characteristic of a metal without the marked signature of superconductivity down to the lowest temperature measured. When the pressure increased to 12.3 GPa, superconducting transition with a T_c value of approximately 5.2 K was observed [Figure 5A]. When the pressure increased to 13.8 GPa, the decrease in electrical resistance became more evident, and the zero-resistance state was fully realized. Moreover, T_c increased rapidly with pressure. Herein, the zero-resistance critical temperature (Tc^zero) and the onset temperature of superconducting transition (Tc^onset) were determined. At > 25.1 GPa, there was a little difference between Tc^zero and Tc^onset, hovering near a width of about 1 K. Herein, the maximum value of Tc was calculated to be approximately 8.2 K at 17.1 GPa, very close to those reported for SnBi₂Te₄ (8.9 K)^[15] and GeSb₂Te₄ (8 K)^[25] under pressure. A comparison of T_c and critical pressures for other TS candidates is shown in Supplementary Table 1.

Figure 5. (A) The temperature dependence of the electrical resistance of SnSb₂Te₄ at various high pressures. (B) The pressure dependence of the critical temperatures Tc^onset and Tc^zero of SnSb₂Te₄. The solid and hollow circles stand for Tc^onset and Tc^zero, respectively. The inset depicts the differential curve dR/dT of the electrical resistance near Tc. The symbols Tc^onset, Tc^mid, and Tc^zero are defined accordingly. Tc^onset refers to the temperature at which the drop in electrical resistance begins; Tc^zero refers to the temperature at which electrical resistance decreases to zero; Tc^mid refers to the temperature at which the maximum of the dR/dT curve occurs.

Figure 5B shows the superconducting phase diagram of the SnSb₂Te₄ powders. Two regions can be distinguished based on the changes in Tc with elevated pressure. At 12.3-17.1 GPa, in which phases II and III coexist, Tc^onset increases monotonically with pressure. The steep slope indicates the strong pressure-induced enhancement of superconductivity. The pressure dependence of Tc at the aforementioned pressure range is similar to that reported in the previous study^[22]. It can be concluded that the positive pressure dependence on Tc observed under pressures of up to 17.1 GPa is correlated to monoclinic C2/m phase II. For Sb₂Te₃^[9] or the binary VA-VIA compound counterparts of SnSb₂Te₄, the evolution of T_C as a function of pressure indicates a positive trend as well. At > 17.1 GPa, the sharp decrease in and the negative pressure dependence of Tc indicate the presence of a new superconducting phase [Figure 5B]. T_C monotonically decreases to 7.2 K at 41.0 GPa. The new superconducting phase corresponds to phase IV (the substitutional solid solution with the bcc structure), which exists at > 17.1 GPa and room temperature. Similar trends in the pressure effect on T_C for the substitutional solid solution phases of Bi₂Te₃^[47], Bi₄Te₃^[48], and SbBi₂Te₄^[15] are also observed. For these materials, superconductivity is depressed by high pressure. As a whole, pressure-driven superconductivity in SnSb₂Te₄ relates closely to the structural phase transitions. The obtained phase diagram reveals a relationship between the structural transition and the appearance of superconductivity.

To ensure the superconducting transition illustrated in Figure 5, we performed electrical resistance measurements near the critical temperature at a varying external magnetic field. The results were shown in Figure 6A with the pressure fixed at 22.3 GPa. It is clear that T_c decreased with increasing magnetic field, confirming that the transition is really superconductive. It is also shown that, with and without a magnetic field, the drop in the electrical resistance is very sharp, indicating bulk and homogeneous occurrence of superconductivity. Figure 6B shows the plot of the temperature dependence of the reduced upper critical field μ₀H(T) (red circles). The data points are fitted to the Werthdamer-Helfand-Hohenberg (WHH) formula^[49]

Figure 6. (A) The temperature dependence of the electrical resistance under various external magnetic fields with the pressure held constant at 22.3 GPa. (B) The temperature dependence of the reduced upper critical field μ₀H(T) (red circles) and the fitting curve according to the WHH formula (green line). The inset shows the dependence of T_c on the external magnetic field. The solid and hollow circles stand for Tc^onset and Tc^zero, respectively.

and the obtained fitting curve (green line) was also shown in Figure 6B. Through extrapolation of the fitting curve, the upper critical field H_c2(0) was estimated to be 3.3 Tesla for H_||c. In the inset of Figure 6B, the variations of the critical temperatures T_C^onset and T_C^zero with magnetic field H were demonstrated.