Hall-coefficient diagnostics of the surface state in pressurized $\mathrm{Sm}{\mathrm{B}}_6$

In this study, we report results of the high-pressure Hall coefficient $\left(R_H\right)$ measurements in the putative topological Kondo insulator $\mathrm{Sm}{\mathrm{B}}_6$ up to 37 GPa. Below 10 GPa, our data reveal that $R_H\left(T\right)$ exhibits a prominent peak upon cooling below 20 K. Remarkably, the temperature at which surface conduction dominates coincides with the temperature of the peak in $R_H\left(T\right)$. The temperature dependent resistance and Hall coefficient can be well fitted by a two-channel model with contributions from the metallic surface and the thermally activated bulk states. When the bulk of $\mathrm{Sm}{\mathrm{B}}_6$ becomes metallic and magnetic at $\sim 10\mathrm{GPa}$, both the $R_H\left(T\right)$ peak and the resistance plateau disappear simultaneously. Our results indicate that the $R_H\left(T\right)$ peak is a fingerprint to diagnose the presence of a metallic surface state in $\mathrm{Sm}{\mathrm{B}}_6$. The high-pressure magnetic state of $\mathrm{Sm}{\mathrm{B}}_6$ is robust to 180 GPa, and no evidence of superconductivity is observed in the metallic phase.

Figure 1

Transport properties in pressurized $\mathrm{Sm}{\mathrm{B}}_6$. (a) Temperature dependence of resistance from 1.7 to 300 K at different pressures in log-log scale. The solid line is the fitting by a two-channel model. (b) Hall coefficient ($R_H$) as a function of temperature measured at different pressures. The inset is the large view of $R_H\left(T\right)$ obtained at higher pressure. Solid lines are the fitting result.

Figure 2

High pressure behavior of metallic $\mathrm{Sm}{\mathrm{B}}_6$. (a) Resistance versus temperature in the pressure range of $9.7\sim 36.8\mathrm{GPa}$ for the sample 1. (b) Temperature dependence of resistance under pressure up to 180 GPa for ample 2. $T^{\prime }$ represents maximum of $dR/dT$ curves indicating the resistance drop in the metallic phase. Samples 1 and 2 were cut from the same batch, which were loaded into the different two high pressure cells for high pressure (∼37 GPa) and very high pressure measurements (∼180 GPa).

Figure 3

High pressure structure information for $\mathrm{Sm}{\mathrm{B}}_6$. (a) X-ray diffraction patterns of $\mathrm{Sm}{\mathrm{B}}_6$ collected at different pressures. (b) and (c) Pressure dependences of lattice parameter and volume. Error bars in (b) are in the brown circles. The volume versus pressure data are fit to the third-order Birch-Murnaghan equation of state [9], as displayed by the solid line in (c). The $B_0$ is the isothermal bulk modulus at ambient pressure, $B_0^{\prime }$ is the pressure derivative of $B_0$ evaluated at zero pressure.

Figure 4

Pressure-temperature phase diagram and Hall coefficient at 1.8 K. (a) Plots of pressure versus characteristic temperatures. P-TKI stands for putative topological Kondo insulator. Pink circles and red squares are the activated gap $\mathit{Eg}$ obtained from temperature-dependent $R-T$ curves and Hall coefficient respectively and is converted to temperature by Eqs. (1) and (2). The olive triangles are the characteristic temperatures $T^{\prime }$ obtained from our R-T curves. Green inverted triangles and cyan rhombuses are the magnetic ordering temperature taken from Ref. [45] (b) Plot of Hall coefficient ($R_H$) versus pressure obtained at 1.8 K. The gray interval indicates the pressure region of insulator-to-metal transition.