Magnetotransport properties of tellurium under extreme conditions

This study investigates the transport properties of a chiral elemental semiconductor tellurium (Te) under magnetic fields and pressure. Application of hydrostatic pressure reduces the resistivity of Te, while its temperature dependence remains semiconducting up to 4 GPa, contrary to recent theoretical and experimental studies. Application of higher pressure causes structural as well as semiconductor-metal transitions. The resulting metallic phase above 4 GPa exhibits superconductivity at 2 K along with a noticeable linear magnetoresistance effect. On the other hand, at ambient pressure, we identified metallic surface states on the as-cleaved ($10\overline{1}0$) surfaces of Te. The nature of these metallic surface states has been systematically studied by analyzing quantum oscillations observed in high magnetic fields. We clarify that a well-defined metallic surface state exists not only on chemically etched samples that were previously reported, but also on as-cleaved ones.

Figure 1

Crystal structure of Te viewed (a) from [0001] direction and (b) from [$10\overline{1}0$] direction. (c) First Brillouin zone of Te. (d) Schematic valence band structure of Te along the direction $k_z$ in the vicinity of the $H$ ($H^{\prime }$) point with spin-orbit interaction. Red and blue colors represent the spin polarization along the [0001] axis. (e) Isoenergetic surfaces of Te at the $H$ ($H^{\prime }$) point. The inner and outer surfaces represent the cases of $E_F<{\epsilon }_0$ and $E_F>{\epsilon }_0$, respectively. (f) Photograph of a Te sample used for transport properties measurements.

Figure 2

(a) Pressure dependence of the resistivity $\rho$ up to 8 GPa at room temperature. (b) Temperature dependence of $\rho$ at various pressures. (c) Temperature dependence of $\rho$ at 5 GPa in magnetic field of 0 and 0.1 T. (d) Magnetic field dependence of $\rho$ up to 5 T at 5 GPa and 1.3 K. The inset shows the magnified view of low-field region up to 0.1 T.

Figure 3

(a) Magnetoresistivity (${\rho }_{xx}$) and (b) Hall resistivity (${\rho }_{yx}$) up to 55 T at several temperatures. (c) FFT spectra of oscillations superimposed on ${\rho }_{xx}$. (d) Magnified view of $d{\rho }_{xx}/dB$ below 12 T. The red arrows indicate the SdH oscillation, discernible only below 6 T. (e) Landau level fan diagram constructed from ${\sigma }_{xx}$ (red) and ${\rho }_{xx}$ (blue). The peaks are plotted for integer $n$. Two SdH components mentioned in the previous data of Berezovets et al. [33] are also shown by closed and open black circles, which are constructed from peaks in $-d^2{\rho }_{xx}/d{B}^2$.

Figure 4

(a) ${\rho }_{xx}$ and (b) ${\rho }_{yx}$ in different magnetic field directions with angles between the magnetic field and the normal vector of ($10\overline{1}0$) surface. The field direction is always normal to the electric current. The data are offset vertically for clarity. (c) Angular dependence of the peak positions in $d{\rho }_{yx}/dB$. The dotted line represents the curve $B_p=A/cos\theta$ for $A=16$ T (red), 21 T (green), and 30 T (blue), respectively.

Figure 5

(a) Conductivity $\sigma =1/\rho$ of samples of different thickness $t$ at 1.4 K and zero magnetic field. (b) Comparison of transverse magnetoresistance normalized by values in zero field.