Decoupling Edge Versus Bulk Conductance in the Trivial Regime of an $\mathrm{InAs}/\mathrm{GaSb}$ Double Quantum Well Using Corbino Ring Geometry

A Corbino ring geometry is utilized to analyze edge and bulk conductance of $\mathrm{InAs}/\mathrm{GaSb}$ quantum well structures. We show that edge conductance exists in the trivial regime of this theoretically predicted topological system with a temperature-insensitive linear resistivity per unit length in the range of $2\mathrm{k}\mathrm{\Omega }/\mu \mathrm{m}$. A resistor network model of the device is developed to decouple the edge conductance from the bulk conductance, providing a quantitative technique to further investigate the nature of this trivial edge conductance, conclusively identified here as being of $n$ type.

Figure 1

(a) Simulated phase diagram (based on actual device geometries—InAs-on-GaSb heterostack reported in Ref. [12] with a 40 nm $\mathrm{H}\mathrm{f}{\mathrm{O}}_2$ top gate dielectric) illustrating the position of two regimes: inverted charge neutrality point (region I—dashed line) and trivial resistance peak (region II with narrow white sector). The contour lines in the electron-rich sectors mark constant electron densities at multiples of $9.66\times {10}^{10}{\mathrm{cm}}^{-2}$, corresponding, at $B=2\mathrm{T}$, to filling of complete Landau levels (b) optical micrograph of a Corbino ring device with top gate lead. Resistance maps at 1.8 K for (c) with edge $R_{1-3;1-3}$ and (d) no edge $R_{1-4;1-4}$ (see text for a definition). Points A–E in (c),(d) indicate gate biases where temperature dependent measurements were performed (see Supplemental Material [24], Sec. II).

Figure 2

Local and nonlocal resistance maps (measured at 1.8 K) at $B=0\mathrm{T}$ (a),(b),(c) and 2 T (e),(f),(g) indicating an edge conductance path at the RPs; (d) and (h) are 1D line cuts at $V_{\mathrm{BG}}=0\mathrm{V}$.

Figure 3

2D maps of extracted bulk and edge resistivities at 1.8 K: (a), (b) at $B=0$ and (c),(d) at $B=2\mathrm{T}$.

Figure 4

Dots in (a) and (b) represent 1D line cuts along $V_{\mathrm{BG}}$ and $V_{\mathrm{TG}}$ directions, respectively, through the 2D map of the extracted edge resistivity [$B=0$ case, Fig. 3]. The lowest cut in each subfigure is shown with its true value, while each consecutive cut is offset vertically by a factor of 10. All dashed lines collectively represent a simple three-parameter fit to the extracted data using an expansion of edge conductivity $1/{\rho }_{\text{edge}}$ up to the first order in ($V_{\mathrm{BG}}$,$V_{\mathrm{TG}}$). Using this global fit, modulation of edge conductance across the domain of reliable extraction exceeds 2x.