Quantum Hall Effect in $n\mathrm{\text{−}}p\mathrm{\text{−}}n$ and $n$-2D Topological Insulator-$n$ Junctions

We have studied quantized transport in HgTe wells with inverted band structure corresponding to the two-dimensional topological insulator phase (2D TI) with locally controlled density allowing $n\mathrm{\text{−}}p\mathrm{\text{−}}n$ and $n$-2D TI-$n$ junctions. The resistance reveals the fractional plateau $2h/e^2$ in the $n\mathrm{\text{−}}p\mathrm{\text{−}}n$ regime in the presence of the strong perpendicular magnetic field. We found that in the $n$-2D TI-$n$ regime the plateaux in resistance in not universal and results from the edge state equilibration at the interface between chiral and helical edge modes. We provided the simple model describing the resistance quantization in $n$-2D TI-$n$ regime.

Figure 1

Schematics of edge state propagation for different charge densities in the central local gate region (red rectangular) and in the regions outside the local gate in the strong magnetic field: (a) $n\mathrm{\text{−}}{n}^{\prime }\mathrm{\text{−}}n$ junction, $n^{\prime }>n$, (b) $n$-2DTI-$n$ junction, (c) $n\mathrm{\text{−}}p\mathrm{\text{−}}n$ junction $n=p$, where $n$ ($p$) refers to negative (positive) charge density. Insets—the energy spectrum for different Fermi energy positions in the region under local gate at $B=0$.

Figure 2

(a) The longitudinal $R_{14,23}$ ($I=1$, 4; $V=3$, 2) resistance as a function of the gate voltage at zero magnetic field (black thick line) and $B=7\mathrm{T}$ (thin red line) in the local gate sample, labeled A; $T=1.4\mathrm{K}$. The inset shows the magnetic field dependence for two gate voltages. (b) The longitudinal $R_{xx}$ ($I=1$, 4; $V=3$, 2) resistance as a function of the gate voltage at zero magnetic field (black thick line) and $B=7\mathrm{T}$ (thin red line), and Hall $R_{xy}$ ($I=1$, 4; $V=2$, 6) resistances in the global gate sample labeled $B$; $T=1.4\mathrm{K}$. The inset shows the magnetic field dependence near CNP. The top panel shows the schematics view of the samples. The perimeter of the gate is shown by the rectangle.

Figure 3

The longitudinal resistance $R_{14,23}$ as a function of the gate voltage and magnetic field, $T=1.4\mathrm{K}$. Two plateaux $R_{14,23}\approx 2\frac{h}{e^2}$ and $R_{14,23}\approx \frac{1}{2}\frac{h}{e^2}$ are indicated by blue arrows. CNP is indicated by the orange arrow.