Nonlocal resistance and its fluctuations in microstructures of band-inverted HgTe/(Hg,Cd)Te quantum wells

We investigate experimentally transport in gated microsctructures containing a band-inverted HgTe/Hg${}_{0.3}$Cd${}_{0.7}$Te quantum well. Measurements of nonlocal resistances using many contacts prove that in the depletion regime the current is carried by the edge channels, as expected for a two-dimensional topological insulator. However, high and nonquantized values of channel resistances show that the topological protection length (i.e., the distance on which the carriers in helical edge channels propagate without backscattering) is much shorter than the channel length, which is $\sim$100 $\mu$m. The weak temperature dependence of the resistance and the presence of temperature dependent reproducible quasiperiodic resistance fluctuations can be qualitatively explained by the presence of charge puddles in the well, to which the electrons from the edge channels are tunnel-coupled.

Figure 1

(a) Scanning electron micrograph of HgTe/HgCdTe structure No. 1. Etched trenches define the Hall bar of a nominal channel width of 5 $\mu$m; the size of the image corresponds roughly to the top gate area. White arrows indicate a monotonous decrease of electrical potential of the contact probes, expected if the current flows only along the edges. Thin yellow arrow shows one of the edge channels. (b) Four-probe longitudinal and Hall resistances as a function of gate voltage for structure No. 1. (c) Local resistance in structure No. 1 for two temperatures.

Figure 2

Nonlocal resistances $R_{ij,kl}$ at 0.46 K vs gate voltage $V_{\mathrm{g}}$, measured for fixed current contacts $\left(ij\right)=\left(82\right)$ and for a series of the voltage probes $\left(kl\right)$ located around structure No. 1. The sign and the additivity of $R_{ij,kl}$ values demonstrate that the current flows only along edges in this range of gate voltages but the magnitudes of $R_{ij,kl}$ are higher than expected for reflectionless channels.

Figure 3

Nonlocal resistance measured for opposite directions of gate voltage sweep showing the reproducible character of resistance fluctuations, and also their quasiperiodicity. (Inset) Spectral density of fluctuations showing the presence of multiple characteristic frequencies. The results are for sample No. 1, but were taken during a different cool-down cycle than the one presented in Fig. 2. The $V_{\text{g}}$ corresponding to QW depletion was observed to significantly vary from one cool-down to another.

Figure 4

(a) Nonlocal resistance fluctuations for four pairs of voltage probe contacts measured in structure No. 2, offset one with respect to another for clarity. (b) The same normalized by the smoothened value of the respective nonlocal resistance. The relative fluctuations of $R_{81,76}$ are clearly distinct from the relative fluctuations of the four other resistances.