Persistence of correlation-driven surface states in ${\mathrm{SmB}}_6$ under pressure

The proposed topological Kondo insulator ${\mathrm{SmB}}_6$ hosts a bulk Kondo hybridization gap that stems from strong electronic correlations and a metallic surface state whose effective mass remains disputed. Thermopower and scanning tunneling spectroscopy measurements argue for heavy surface states that also stem from strong correlations, whereas quantum oscillation and angle-resolved photoemission measurements reveal light effective masses that would be consistent with a Kondo breakdown scenario at the surface. Here we investigate the evolution of the surface state via electrical and thermoelectric transport measurements under hydrostatic pressure, a clean symmetry-preserving tuning parameter that suppresses the Kondo gap and increases the valence of Sm from ∼2.6+ towards a 3+ magnetic metallic state. Electrical resistivity measurements reveal that the surface carrier density increases with increasing pressure, whereas thermopower measurements show an unchanged Fermi energy under pressure. As a result, the effective mass of the surface state charge carriers linearly increases with pressure as the Sm valence approaches 3+. Our results are consistent with the presence of correlation-driven surface states in ${\mathrm{SmB}}_6$ and suggest that the surface Kondo effect persists under pressure to 2 GPa.

Figure 1

(a) Temperature dependence of the electrical resistivity on the (001) plane of ${\mathrm{SmB}}_6$ under applied pressure. Solid lines are fits to a two-channel model described in the text. (b) Pressure dependence of the carrier density $n_s$ of the surface state in ${\mathrm{SmB}}_6$ from the two-channel model fits.

Figure 2

(a),(b) Pressure dependence of the carrier density $n_{b0}$ and mobility ${\mu }_b$ of the bulk contribution from the two-channel model fits. Error bars are representative. (c) Pressure dependence of the bulk energy gap parameter ${\mathrm{\Delta }}_b$ from a two-channel model fit.

Figure 3

(a) Temperature dependence of thermopower $S$ for ${\mathrm{SmB}}_6$ at pressures to 2 GPa. The inset is a magnified view below crossover temperature T* where the surface contribution dominates. The dashed line indicates the slope of thermopower at low temperature with $S/T\approx -6.0\left(2\right)\mathit{\mu }V/{\mathrm{K}}^2$. (b) Pressure dependence of the effective mass of ${\mathrm{SmB}}_6$ surface state quasiparticles, normalized by its value at ambient pressure. (c) Schematic sketch of the band structures of ${\mathrm{SmB}}_6$ at ambient pressure (left) and high pressure (right). Valence and conduction bands remain qualitatively unchanged, but the energy gap $\mathrm{\Delta }$ is reduced with pressure. Red lines indicate band dispersion for surface states within the bulk insulating gap. For purposes of illustration, the relative flattening of bulk and surface states under pressure is exaggerated.

Figure 4

(a)–(c) Temperature dependence of resistivity ${\rho }_{xx}$ (squares) and Hall coefficient $R_H$ (circles) plotted on the left and right ordinates, respectively, for pressures of 1.1 GPa (a), 2.1 GPa (b), and 3.2 GPa (c).The solid lines are fits to a two-channel model. Data are from Zhou et al. in Ref. [41]. (d) Pressure dependence of the carrier density $n_s$ of the surface state and the inverse Hall coefficient $-1/R_{\mathrm{H}}$ plotted on the left and right ordinates, respectively. Data are normalized at $P=1\mathrm{GPa}$. The solid squares indicate $n_s$ in this study. Error bars are smaller than the size of the data points. The solid circles indicate $n_s$ from the two-channel model fit, and the open triangles indicate $-1/R_{\mathrm{H}}$ at 1.8 K taken from (a)–(c).