Magnetotransport measurements of the surface states of samarium hexaboride using Corbino structures

The recent conjecture of a topologically protected surface state in ${\mathrm{SmB}}_6$ and the verification of robust surface conduction below 4 K have prompted a large effort to understand surface states. Conventional Hall transport measurements allow current to flow on all surfaces of a topological insulator, so such measurements are influenced by contributions from multiple surfaces of varying transport character. Instead, we study magnetotransport of ${\mathrm{SmB}}_6$ using a Corbino geometry, which can directly measure the conductivity of a single, independent surface. Both (011) and (001) crystal surfaces show a strong negative magnetoresistance at all magnetic field angles measured. The (011) surface has a carrier mobility of $122{\text{cm}}^2/\text{V}·\text{s}$ with a carrier density of $2.5\times {10}^{13}{\text{cm}}^{-2}$, which are significantly lower than indicated by Hall transport studies. This mobility value can explain the failure so far to observe Shubnikov–de Haas oscillations. Analysis of the angle dependence of conductivity on the (011) surface suggests a combination of a field-dependent enhancement of the carrier density and a suppression of Kondo scattering from native oxide layer magnetic moments as the likely origin of the negative magnetoresistance. Our results also reveal a hysteretic behavior whose magnitude depends on the magnetic field sweep rate and temperature. Although this feature becomes smaller when the field sweep is slower, it does not disappear or saturate during our slowest sweep-rate measurements, which is much slower than a typical magnetotransport trace. These observations cannot be explained by quantum interference corrections such as weak antilocalization but are more likely due to an extrinsic magnetic effect such as the magnetocaloric effect or glassy ordering.

Figure 1

Magnetoresistance traces at several angles for (a) the (011) surface and (b) the (001) surface. Angle dependence of the ratio (squares) of the resistance with an out-of-plane field ($R$) to the resistance with an in-plane field ($R_{\parallel }$) for (c) the (011) surface and (d) the (001) surface at representative magnetic fields, along with ${cos}^2\theta$ fits (lines). The ratio $R/R_{\parallel }$ is plotted vs the magnetic field for (e) the (011) and (f) the (001) surfaces.

Figure 2

The (011) surface carrier density (filled squares) and mobility (open diamonds) obtained from angle-dependent fits of the data. Shaded areas represent uncertainty in the parameters of the angle-dependent fits. Best-fit curves for the polynomial $n\left(B\right)$ [lower two (blue) lines] and corresponding $\mu \left(B\right)$ [upper two (red) lines] using the $\theta ={25}^{\circ }$ and $\theta ={85}^{\circ }$ data (solid lines) and using the $\theta =5^{\circ }$ and $\theta ={85}^{\circ }$ data (dashed lines). The vertical log scale allows direct comparison of the relative magnitudes of changes in $n$ and $\mu$.

Figure 3

Response of the resistivity of Corbino disk samples to the magnetic field at different sweep rates below 6 T at $0.3\text{K}$. Numbers shown close to each curve are the magnetic field sweep-rate magnitude (in units of mT/s). Inset: Example of a Corbino disk sample image prepared on a polished ${\mathrm{SmB}}_6$ surface.

Figure 4

Response of the resistivity of Corbino disk samples to the magnetic field at different sweep rates below 1 T at 80 mK: (a) (001) sample; (b) (011) sample.

Figure 5

Magnitude of the dips (in conductivity) as a function of the temperature at a magnet field sweep rate of $0.167$ mT/s.

Figure 6

Magnitude of the dips (in conductivity) as a function of the magnet field sweep rate at 80 mK.

Figure 7

Response of the resistivity of Corbino disk samples to the magnetic field, comparing at different angles of the magnetic field at $0.3$ K. The solid curve is the magnetic field perpendicular to the transport surface. The dotted curve is the magnetic field parallel to the transport surface. The minimal points are shifted to $B$ = 0 T for direct comparison.

Figure 8

Resistivity vs temperature for (a) the (011) surface and (b) the (001) surface. The solid black line represents data; long-dashed (red) lines, logarithmic fits on a linear temperature background; and the short-dashed (green) line, a logarithmic fit on a quadratic temperature background.

Figure 9

Fitted mobility, alongside several mobility projections of the Kondo effect for various $T_K$ values.

Figure 10

Cosine fits (solid curves) of angle-dependent magnetoresistance data [(red) squares] at a 5-, 12-, and 25-T magnetic field, respectively, for (a–c) the (001) surface and (d–f) the (011) surface.

Figure 11

The (001) surface carrier density (filled squares) and mobility (open diamonds) obtained from angle-dependent fits of the data. Shaded areas represent uncertainty in the parameters of the angle-dependent fits. The vertical log scale allows direct comparison of the relative magnitudes of changes in $n$ and $\mu$ and is proportional to that in Fig. 2. We warn the reader that these values are not reliable, as discussed in the text.

Figure 12

Simulated magnetoresistance of the (011) surface due to Kondo scattering alone, based on the values obtained from the logarithmic temperature dependence. Simulations for Kondo temperatures of 20 K [dash-dotted (red) curve] and 40 K [dotted (blue) curve] are shown alongside the actual magnetoresistance obtained from measurements (solid black curve).