Tuning Bulk and Surface Conduction in the Proposed Topological Kondo Insulator ${\mathrm{SmB}}_6$

Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo-insulator compound ${\mathrm{SmB}}_6$ are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single (100) surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The surface conductance, on the order of $100e^2/h$, exhibits a field-effect mobility of $133{\mathrm{cm}}^2/\mathrm{Vs}$ and a large carrier density of $\sim 2\times {10}^{14}{\mathrm{cm}}^{-2}$, in good agreement with recent photoemission results. With the ability to gate modulate surface conduction by more than 25%, this approach provides promise for both fundamental and applied studies of gate-tuned devices structured on bulk crystal samples.

Figure 1

(a) Electrical resistance of a single crystal of ${\mathrm{SmB}}_6$ as a function of sample thickness, normalized to its value at 20 K. The solid lines represent fits to the data using a two-channel conductance model [Eq. (1)], with fit parameters including the surface (b) and bulk (c) resistance ratio components $r_s\equiv R_s/R(20\mathrm{K})$ and $r_b\equiv R_b/R(20\mathrm{K})$, respectively, of the total conductance. [Note that the geometry of sample for each 0.0325 mm thickness data set in (a) is slightly different due to loss of sample fraction.]

Figure 2

(a) Electrical resistance of ${\mathrm{SmB}}_6$ sample as a function of ionic liquid gate voltage, measured with a Corbino disk lead geometry placed on the surface of a single crystal, as shown in the inset (superimposed on sample photograph, with green shaded area representing the area covered by the ionic liquid gate structure). Solid lines are fits to the two-channel conductance model [Eq. (2)]. Panels (b) and (c) present the surface and bulk resistance contributions, respectively, extracted from the two-channel fits as a function of gate voltage. (d) Transient current between the gate pad and ground as a function of gate voltage sweep rate, measured at 230 K. The solid line is a fit to a charging capacitor model with a capacitance of 14.4 nF. (e) Two-dimensional sheet conductivity as a function of the change in carrier concentration induced by gating. The solid line is a fit to a constant-mobility model with a mobility $\mu =133{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$.

Figure 3

(a) Evolution of the crossover temperature $T^{*}$ between bulk- and surface-dominated conductance, defined as the inflection point in resistance temperature dependence as a function of (a) crystal thickness variation and (b) ionic liquid gate voltage tuning. The nonconstant evolution of $T^{*}$ is consistent with the two-channel conduction model (see text), showing that the crossover depends solely on the relative bulk and surface contributions to the total electrical conduction.