Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction

We analyze the dynamics of the helical edge modes of a quantum spin Hall state in the presence of a spatially nonuniform Rashba spin-orbit (SO) interaction. A randomly fluctuating Rashba SO coupling is found to open a scattering channel which causes localization of the edge modes for a weakly screened electron-electron ($e\mathrm{\text{−}}e$) interaction. A periodic modulation of the SO coupling, with a wave number commensurate with the Fermi momentum, makes the edge insulating already at intermediate strengths of the $e\mathrm{\text{−}}e$ interaction. We discuss implications for experiments on edge state transport in a HgTe quantum well.

Figure 1

The edge localization length ${\xi }_{\mathrm{loc}}$ for different values of the interaction parameter $K_0$. The dashed line marks the length of a micron-sized HgTe QW sample [9].

Figure 2

The gap $\Delta$ for different Rashba amplitudes $\hslash A$ and values of $K_0$ (with the curves sorted from left to right with increasing $\hslash A$). The circles and squares mark the smallest gaps for HgTe QW samples of length $1\mu \mathrm{m}$ and $20\mu \mathrm{m}$, respectively.