Tuning Edge States in Strained-Layer $\mathrm{InAs}/\mathrm{GaInSb}$ Quantum Spin Hall Insulators

We report on a class of quantum spin Hall insulators (QSHIs) in strained-layer $\mathrm{InAs}/\mathrm{GaInSb}$ quantum wells, in which the bulk gaps are enhanced up to fivefold as compared to the binary $\mathrm{InAs}/\mathrm{GaSb}$ QSHI. Remarkably, with consequently increasing edge velocity, the edge conductance at zero and applied magnetic fields manifests time reversal symmetry-protected properties consistent with the $Z_2$ topological insulator. The $\mathrm{InAs}/\mathrm{GaInSb}$ bilayers offer a much sought-after platform for future studies and applications of the QSHI.

Figure 1

Calculated band dispersions and wafer structures of the strained $\mathrm{InAs}/\mathrm{GaInSb}$ QWs. [(a)–(c)] Calculated bulk band structure of the $\mathrm{InAs}/{\mathrm{Ga}}_{0.80}{\mathrm{In}}_{0.20}\mathrm{Sb}$ ($8.7/4\mathrm{nm}$) QWs, $\mathrm{InAs}/{\mathrm{Ga}}_{0.75}{\mathrm{In}}_{0.25}\mathrm{Sb}$ ($9/4\mathrm{nm}$) QWs, and $\mathrm{InAs}/{\mathrm{Ga}}_{0.68}{\mathrm{In}}_{0.32}\mathrm{Sb}$ ($8/4\mathrm{nm}$) QWs; CB1, VB1 and CB2, VB2 are bands of different spin component. (d) Schematic drawing of band dispersion (both bulk states and edge states) in the $\mathrm{InAs}/\mathrm{GaInSb}$ QSHI system. (e) Wafer structures of the strained-layer $\mathrm{InAs}/{\mathrm{Ga}}_{0.75}{\mathrm{In}}_{0.25}\mathrm{Sb}$ QWs used for experiments. (f) Shown here as an example, a TEM photograph of the strained $\mathrm{InAs}/{\mathrm{Ga}}_{0.68}{\mathrm{In}}_{0.32}\mathrm{Sb}$ wafer; blue and red lines are a guide for the eyes.

Figure 2

Transport data of bulk states from Corbino devices. $G\text{−}{V}_{\text{front}}$ traces of a $\mathrm{InAs}/{\mathrm{Ga}}_{0.75}{\mathrm{In}}_{0.25}\mathrm{Sb}$ Corbino under different in-plane magnetic field at (a) $V_{\mathrm{back}}=0\mathrm{V}$ and (b) $V_{\mathrm{back}}=4\mathrm{V}$. $G\text{−}{V}_{\text{front}}$ traces under different perpendicular magnetic fields at (c) $V_{\mathrm{back}}=0\mathrm{V}$ and (d) $V_{\mathrm{back}}=4\mathrm{V}$. $G\text{−}{V}_{\text{front}}$ traces under different in-plane magnetic fields for (e) a $\mathrm{InAs}/{\mathrm{Ga}}_{0.80}{\mathrm{In}}_{0.20}\mathrm{Sb}$ Corbino and (f) a $\mathrm{InAs}/{\mathrm{Ga}}_{0.68}{\mathrm{In}}_{0.32}\mathrm{Sb}$ Corbino. (g) Arrhenius plots for $\mathrm{InAs}/\mathrm{GaSb}$ QWs (open squares), $\mathrm{InAs}/{\mathrm{Ga}}_{0.80}{\mathrm{In}}_{0.20}\mathrm{Sb}$ QWs (open circles), $\mathrm{InAs}/{\mathrm{Ga}}_{0.75}{\mathrm{In}}_{0.25}\mathrm{Sb}$ QWs (filled diamonds), and $\mathrm{InAs}/{\mathrm{Ga}}_{0.68}{\mathrm{In}}_{0.32}\mathrm{Sb}$ QWs (filled circles). Energy gaps are deduced by fitting $G_{xx}\propto \exp (-\mathrm{\Delta }/2k_{B}T)$, as shown by straight dash lines in the plot. Here $k_B$ is the Boltzmann constant.

Figure 3

Helical edge transport in strained-layer $\mathrm{InAs}/{\mathrm{Ga}}_{0.75}{\mathrm{In}}_{0.25}\mathrm{Sb}$ QWs. $R_{xx}\text{−}{V}_{\text{front}}$ traces measured from (a) a $100\times 50\mu \mathrm{m}$ Hall bar device and (b) a $10\times 5\mu \mathrm{m}$ Hall bar device at $T\sim 20\mathrm{mK}$ with $V_{\mathrm{back}}=0$, 1, 2, 3, and 4 V. The edge characteristic length increases with decreasing $V_{\mathrm{back}}$. The inset in (a) shows the ${\lambda }_{\phi }$ and the $n_{\text{cross}}$ values at different back-gate bias $V_{\mathrm{back}}$.

Figure 4

Helical edge conductance under magnetic field. (a) $R_{xx}\text{−}{V}_{\text{front}}$ traces of a $3\times 1.5\mu \mathrm{m}$ Hall bar under different perpendicular magnetic field ($V_{\mathrm{back}}=0\mathrm{V}$). Inset in (a): the $R_{\mathrm{CNP}}$ values increase monotonically in the range of $B_{\perp }<5\mathrm{T}$, manifesting enhanced backscattering processes in the helical edge under TRS breaking. (b) $R_{xx}\text{−}{V}_{\text{front}}$ traces of the $3\times 1.5\mu \mathrm{m}$ Hall bar under different in-plane magnetic fields. The plateau resistance values rise above the quantized value under $B_{//}$ because of TRS breaking. $R_{xx}\text{−}{V}_{\text{front}}$ traces of the $100\mu \mathrm{m}\times 50\mu \mathrm{m}$ Hall bar under different perpendicular magnetic field at (c) $V_{\mathrm{back}}=0\mathrm{V}$ and (d) $V_{\mathrm{back}}=4\mathrm{V}$.