Transport in disordered two-dimensional topological insulators

The transport properties of the “inverted” semiconductor HgTe-based quantum well, recently shown to be a two-dimensional topological insulator, are studied experimentally in the diffusive regime. Nonlocal transport measurements are performed in the absence of magnetic field, and a large signal due to the edge states is observed. This shows that the edge states can propagate over a long distance, $\sim$1 mm, and therefore, there is no difference between local and nonlocal electrical measurements in a topological insulator. In the presence of an in-plane magnetic field a strong decrease of the local resistance and complete suppression of the nonlocal resistance is observed. We attribute this behavior to an in-plane magnetic-field-induced transition from the topological insulator state to a conventional bulk metal state.

Figure 1

Schematic top view of the central part of the sample, covered by the gate (shown in blue or light grey) (a) Red thin lines are edge states localized at the periphery of the sample under a TiAu metallic gate in the TI state. Red areas are the regions with $n$-type HgTe. (b) The diagonal $R_{xx}$ (thick line, $I=1,6$, $V=9,8$) and Hall $R_{xy}$(dotted line, $I=1,6$, $V=9,3$) resistances as a function of the gate voltage at zero and fixed magnetic field. The inset shows the temperature dependence of the peak at zero magnetic field. Two traces at zero field are shown in (b) (red solid line, $T=1$ K; blue dashed line, $T=0.08$ K).

Figure 2

(a) Local and (b, c) nonlocal resistances at zero magnetic field as a function of the gate voltage for different configurations, which are shown in the top panel. Red (grey) lines represent a 1D wire along the sample edge. The inset in (a) shows the local and nonlocal resistance in the region with bulk dissipative transport. $T=80$ mK.

Figure 3

(a) Local resistance as a function of the perpendicular magnetic field for different gate voltages. Thick traces are taken for the electronic part of the TI peak,$V_g=-2.5$ to $-$3.8 V, step of 0.1 V. Thin traces are taken for the hole part of the TI peak, $V_g=-3.8$ to $-4.8$ V, step of $0.1$ V. (b) Nonlocal resistance as a function of the perpendicular magnetic field for different gate voltages. Thick traces are taken for the electronic part of the TI peak, $V_g=-2.5$ to $-3.8$ V, step of 0.2 V. Thin traces are taken for the hole part of the TI peak, $V_g=-3.8$ to $-4.8$ V, step of 0.1 V. $T=80$ mK.

Figure 4

(a) Local resistance as a function of in-plane magnetic field for different gate voltages. Thick traces are taken for the electronic part of the TI peak, $V_g=-2.5$ to $-3.7$ V, step of 0.1 V. Thin traces are taken for the hole part of the TI peak, $V_g=-3.8$ to $-4.0$ V, step of 0.1 Volts. (b) Nonlocal resistance as a function of in-plane magnetic field for different gate voltages. Thick traces are taken for the electronic part of the TI peak, $V_g=-3.5$ to $-3.8$ V, step of 0.1 V. Thin traces are taken for the hole part of the TI peak, $V_g=-3.9$ to $-4.1$ V, step of 0.1 Volts. $T=80$ mK.