Superconductivity and critical fields of tellurium single crystal under high pressure

Tellurium (Te) is one of the $p$-orbital chalcogens, which shows attractive physical properties at ambient pressure. Here, we systematically investigate both structural and electronic evolution of Te single crystal under high pressure up to 40 GPa. The pressure dependence of the experimental Raman spectrum reveals the occurrence of multiple phase transitions, which is consistent with high-pressure synchrotron x-ray diffraction measurements. The appearance of superconductivity in high-pressure phase of Te is accompanied by structural phase transitions. The high-pressure phases of Te reveal a nonmonotonic evolution of superconducting temperature $T_c$ with notably different upper critical fields. The theoretical calculations demonstrate that the pressure dependence of the density of states agrees well with the variation of $T_c$. Our results provide a systematic phase diagram for the pressure-induced superconductivity of Te.

Figure 1

The crystal structure and Raman spectroscopy of Te under high pressures. (a) The crystal structures of Te-I, Te-II, Te-III, Te-V with $c$ axis. (b) Pressure dependence of Raman spectra under various pressures for Te at room temperature. (c) Raman shifts of Te in compression. The colored backgrounds show different phases of Te, as summarized in Table 1.

Figure 2

Electrical resistivity of Te as a function of temperature for various pressures. The insets of each figures show temperature-dependent resistivity of Te in the vicinity of the superconducting transition. The red line in (d) shows the resistivity data under decompression to 31.4 GPa.

Figure 3

Temperature dependence of resistivity under different magnetic fields for Te at (a) 4.5 GPa, (b) 17.5 GPa, and (c) 34.8 GPa, respectively. (d) Estimated upper critical field for Te. Here, $T_c$ is determined as a 90% drop in the normal-state resistivity. The solid lines represent fits based on the formula (1).

Figure 4

$M\text{−}T$ curves at (a) 6.0 GPa and at (b) 8.9 GPa. The hollow symbols show the FC curves and the solid symbols show the ZFC curves. The insets show the fitted results of $H_{c1}$ from $M\text{−}H$ measurements.

Figure 5

Electronic band structure and density of states (DOS) of Te at various pressures. The electronic structures of the four phases from DFT results are shown. In each figure, the left graphs show the band structure and the right graphs show the DOS, with the vertical axis representing energy in $E-E_F$ and the horizontal axis representing DOS per atom in a unit cell.

Figure 6

Electronic phase diagram for Te under pressures. The colored areas represent different phases. The top panel shows the pressure dependence of the calculated band gaps of Te-I, and the density of states (DOS) at the Fermi level for Te-II, Te-III, and Te-V. The bottom panel shows the superconducting $T_c$ as a function of pressure. The solid symbols represent the $T_c$ extracted from different runs of resistivity measurements.