Localization of trivial edge states in InAs/GaSb composite quantum wells

The InAs/GaSb heterostructure is one of the systems where the quantum spin Hall effect is predicted to arise. However, as confirmed by recent experimental studies, the most significant highlight of the effect, i.e., conductance quantization due to nontrivial edge states, is obscured by spurious conductivity arising from trivial edge states. In this Rapid Communication, we present an experimental observation of the strong localization of trivial edge modes in an InAs/GaSb heterostructure which was weakly disordered by silicon deltalike dopants within the InAs layer. The edge conduction which is characterized by a temperature-independent behavior at low temperatures and a power law at high temperatures is observed to be exponentially scaled with the length of the edge. Comprehensive analyses on measurements with a range of devices is in agreement with the localization theories in quasi-one-dimensional electronic systems.

Figure 1

(a) Longitudinal resistance of the Hall bar device as a function of $V_{tg}$ and $V_{bg}$ measured at $T=10$ mK applying 10-nA DC current. The inset shows the optical microscope image of the device with a 5-$\mu \text{m}$ black scale bar. (b) Density modulation via the top gate obtained from Hall measurements at 0.5 T (red curve). The dashed guideline indicates the zero density. The black curve shows the corresponding longitudinal resistance at $B=0$. (c) Longitudinal and transverse resistances as a function of $B$ measured at 10 mK. As a signature of high mobility, clear SdH oscillations and quantum Hall plateaus are observed. The carrier densities calculated from quantum Hall and SdH oscillations are consistent with the one obtained from the classical Hall effect in (b).

Figure 2

(a) Nonlocal resistance measured in the Hall bar device as a function of top and bottom gate voltages at 10 mK. The inset shows the optical image of the device with labeled contacts. $R_{ij,kl}$ is the resistance measured between $k$ and $l$ when the current is applied between $i$ and $j$. (b) Comparison of local and two different configurations of nonlocal resistances as functions of the top gate voltage.

Figure 3

Temperature behavior of the minimum bulk conductivity measured in the Corbino disk with 100-$\mu \mathrm{V}$ AC bias for different bottom gate voltages. The solid lines are the fits to the Arrhenius equation giving the corresponding bulk gap for each bottom gate voltage.

Figure 4

Edge component of the Hall bar conductance minima in top gate sweeps as a function of temperature. A power-law behavior with an average exponent $\alpha =0.65\pm 0.05$ at high temperatures (solid lines) and saturated conductance at low temperatures are observed. The dashed line represents $T=(\gamma /2\pi )V$ with $\gamma =0.1$. The inset illustrates the power-law scaling of the conductance with voltage excitation at lowest temperatures, with a corresponding power exponent $\beta =1.25\pm 0.02$.

Figure 5

The conductance minimum vs edge length measured in the finger gated device. The optical microscope image is shown in the inset, and the black scale bar indicates 10-$\mu \text{m}$ length.