Interface-Induced Topological Insulator Transition in $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ Quantum Wells

We demonstrate theoretically that interface engineering can drive germanium, one of the most commonly used semiconductors, into a topological insulating phase. Utilizing giant electric fields generated by charge accumulation at $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ opposite semiconductor interfaces and band folding, the new design can reduce the sizable gap in Ge and induce large spin-orbit interaction, which leads to a topological insulator transition. Our work provides a new method to realize topological insulators in commonly used semiconductors and suggests a promising approach to integrate it in well-developed semiconductor electronic devices.

Figure 1

(a) Schematic of the structure of an ultrathin Ge layer sandwiched by thick GaAs layers (the upper left-hand panel). The upper right-hand panel amplifies the atomic configuration of the $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ quantum well containing four bilayer Ge. Notice that the Ga and As atoms locate at the opposite interfaces which leads to a charge accumulation schematically shown in the left-hand panel. (b) The BZ of bulk Ge and the folded BZ of $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ QW along the [111] crystallographic direction. (c) The charge accumulation at two opposite interfaces obtained from the first-principles calculation. The red and green isosurfaces describe the positive and negative charge accumulations at opposite interfaces.

Figure 2

(a) Band structures of $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ sandwiched structures with different Ge portions obtained from the first-principles HSE calculations. From left to right, two Ge bilayers, four Ge bilayers, and four Ge bilayers with 3% in-plane tensile strain. (b) The band gap (purple line with diamonds) and the inner polarization field strength (blue line with squares) as functions of the number of Ge bilayers. (c) The variation of band gap $\Delta E_g=E_g^{\mathrm{strain}}-E_g$ as a function of in-plane strain.

Figure 3

(a) Band structures of a $\mathrm{GaAs}/\mathrm{Ge}/\mathrm{GaAs}$ QW structure with 18 Å Ge layer thickness obtained from the 30-band $\mathbf{k}·\mathbf{p}$ model. The inset shows the Rashba spin splitting (RSS) of electron, heavy hole (HH), and light hole (LH). (b) Band structure of the quantum wire obtained by solving the effective four-band model. The gapless edge states are shown by the red line. The central inset shows the schematic of the quantum wire and the helical edge states. The right (red) and left peaks (blue) describe the density distribution of the spin-up and spin-down edge states at $k_{\parallel }=-0.01{\AA }^{-1}$, respectively.