Low-temperature surface conduction in the Kondo insulator SmB${}_6$

We study the transport properties of the Kondo insulator SmB${}_6$ with a specialized configuration designed to distinguish bulk-dominated conduction from surface-dominated conduction. We find that as the material is cooled below 4 K, it exhibits a crossover from bulk to surface conduction with a fully insulating bulk. We take the robustness and magnitude of the surface conductivity, as is manifest in the literature of SmB${}_6$, to be strong evidence for the topological insulator metallic surface states recently predicted for this material.

Figure 1

(a) A schematic diagram of a piece of SmB${}_6$ with eight coplanar contacts, four on each side, sandwiched between two silicon wafer pieces with gold contact pads. (b) A scanning electron microscope image of a single crystal of SmB${}_6$, sandwiched between two silicon wafer pieces with lithographically defined contact pads. Inset: a close-up of one of the platinum contacts connecting the SmB${}_6$ to a gold contact pad.

Figure 2

A logarithmic plot of 3D resistivity $G_{\mathrm{measured}}$ (solid blue line) vs inverse temperature. A linear model of the plateau conductance $G_{\mathrm{plateau}}$ (dash-dotted line) is removed from $G_{\mathrm{measured}}$ to extrapolate (red line) the bulk resistivity to 3 K. A linear fit (dashed line) yields an activation energy of 3.47 meV.

Figure 3

A cross section of the sample along the electrical contacts. Arrows indicate current direction; lines indicate equipotentials. (a) Current passes vertically through the bulk, far away from the voltage contacts. (b) The bulk in (a) becomes insulating, forcing the current to flow around the edge. The surface potential is indicated by the thickness of the orange region. (c) Current passes laterally through the bulk, and the front-side and back-side voltages are measured at similar equipotentials. (d) The bulk in (c) becomes insulating, isolating the back-side contacts from the majority current flow.

Figure 4

Simulated log-log plots of the four-terminal resistances as a function of temperature. Left: the case where the saturation conductivity is a bulk phenomenon. Right: the case where the saturation conductivity is a surface conductivity.

Figure 5

A log-log plot of $R_{\mathrm{lat}}$ (solid), $R_{\mathrm{vert}}$ (dash-dotted), and $R_{\mathrm{hyb}}$ (dotted) as a function of temperature. Inset: a linear plot of $R_{\mathrm{lat}}$ and $R_{\mathrm{hyb}}$, emphasizing the divergence between them between 3 and 5 K.