Low-temperature conductivity of weakly interacting quantum spin Hall edges in strained-layer InAs/GaInSb

We report low-temperature transport measurements in strained $\mathrm{InAs}/\mathrm{G}{\mathrm{a}}_{0.68}\mathrm{I}{\mathrm{n}}_{0.32}\mathrm{Sb}$ quantum wells, which supports time-reversal symmetry-protected helical edge states. The temperature and bias voltage dependence of the helical edge conductance for devices of various sizes are consistent with the theoretical expectation of a weakly interacting helical edge state. Moreover, we found that the magnetoresistance of the helical edge states is related to the edge interaction effect and the disorder strength.

Figure 1

Transport results of bulk states. (a) The solid line shows the $R_{xx}\text{−}{V}_{\mathrm{back}}$ trace of a 75 μm × 25 μm Hall bar made by the $\mathrm{InAs}/\mathrm{G}{\mathrm{a}}_{0.68}\mathrm{I}{\mathrm{n}}_{0.32}\mathrm{Sb}$ QWs. Squares are the electron densities obtained from SdH oscillations, and the dashed line is the linear fitting of the electron densities. (b), (c), and (d) show the temperature dependence, bias voltage dependence, and in-plane magnetic field dependence of a Corbino device (inner/outer diameter 800/1200 μm), respectively. The bias voltage used for (b) and (d) is 0.1 mV. The ac modulation voltage used for (c) is 50 μV.

Figure 2

Temperature and bias dependence measurement of the helical edge conductance. $R_{xx}\text{−}{V}_{\mathrm{front}}$ traces of the $12\mu \mathrm{m}\times 4\mu \mathrm{m}$ Hall bar (a) measured with 0.1, 1, and 10 nA bias current at 30 mK, respectively; (b) measured at 50 mK, 500 mK, and 2 K biased with 0.1 nA current, respectively. The inset of (b) shows the $G_{\mathrm{edge}}$ (conductance of the averaged $R_{xx}$ peaks) versus $T$. (c) and (d) illustrate that for the single-edge device and the 5 μm length two-terminal device, the quantized $R_{xx}$ plateau is independent of $T$ and $V$ within a certain range. The schematic drawings of the device configuration are also shown in the figure. For the single-edge device, two contacts separated by 1.2 μm served as both the current leads and the voltage probes.

Figure 3

Response to external magnetic fields. $R_{xx}\text{−}{V}_{\mathrm{front}}$ traces of (a) the $12\mu \mathrm{m}\times 4\mu \mathrm{m}$ Hall bar and (b) the 1.2 μm single-edge device measured with 0.1 nA under $B=0\mathrm{T},B_{\parallel }=1\mathrm{T}$, and $B_{\perp }=1\mathrm{T}$, respectively. (c) Bias voltage dependence of the differential $R_{\mathrm{edge}}$ for the $12\mu \mathrm{m}\times 4\mu \mathrm{m}$ Hall bar under $B=0\mathrm{T}$ (square), $B_{\parallel }=2\mathrm{T}$ (circle), and $B_{\perp }=1\mathrm{T}$ (triangle) at 30 mK, respectively. The ac modulation current used for measurements is 0.1 nA. (d) Temperature dependence of the $R_{\mathrm{edge}}$ for the $12\mu \mathrm{m}\times 4\mu \mathrm{m}$ Hall bar under $B=0\mathrm{T}$ (square), and $B_{\parallel }=2\mathrm{T}$ (circle), respectively.

Figure 4

Magnetoresistance of helical edge states. (a) $R_{\mathrm{edge}}$ of a 30 μm × 10 μm Hall bar made by a strongly interacting InAs/GaSb QW as a function of magnetic fields, measured with 1 and 100 nA excitation current at 300 mK, respectively. (b) $R_{\mathrm{edge}}$ of a 30 μm × 10 μm Hall bar made by the $\mathrm{InAs}/\mathrm{G}{\mathrm{a}}_{0.68}\mathrm{I}{\mathrm{n}}_{0.32}\mathrm{Sb}$ QWs as a function of $B_{\perp }$ with 0.5, 5, and 50 nA bias current at 300 mK, respectively. (c) $R_{\mathrm{edge}}$ of the 75 μm × 25 μm Hall bar made by the $\mathrm{InAs}/\mathrm{G}{\mathrm{a}}_{0.68}\mathrm{I}{\mathrm{n}}_{0.32}\mathrm{Sb}$ QWs as a function of $B_{\parallel }$ with 0.1 and 1 nA bias current at 300 mK. (d) Normalized edge magnetoresistance of several samples made by the $\mathrm{InAs}/\mathrm{G}{\mathrm{a}}_{0.68}\mathrm{I}{\mathrm{n}}_{0.32}\mathrm{Sb}$ QWs with different $L$ and $l_{\phi }$. The aspect ratio (length/width) of all four samples is 3.