Inelastic Electron Backscattering in a Generic Helical Edge Channel

We evaluate the low-temperature conductance of a weakly interacting one-dimensional helical liquid without axial spin symmetry. The lack of that symmetry allows for inelastic backscattering of a single electron, accompanied by forward scattering of another. This joint effect of weak interactions and potential scattering off impurities results in a temperature-dependent deviation from the quantized conductance, $\delta G\propto T^4$. In addition, $\delta G$ is sensitive to the position of the Fermi level. We determine numerically the parameters entering our generic model for the Bernevig-Hughes-Zhang Hamiltonian of a $\mathrm{HgTe}/\mathrm{CdTe}$ quantum well in the presence of Rashba spin-orbit coupling.

Figure 1

Dimensionless factor $f(\zeta )=f(v_F{k}_F/T)$ describing the dependence of the interaction-induced conductance correction on the Fermi momentum; see Eq. (9).

Figure 2

Representative one-particle backscattering process to second order in the electron-electron interaction (wavy line) and impurity scattering (cross).

Figure 3

Off-diagonal component $[B_{k_1}^{†}{B}_{k_2}{]}^{-+}$ of the spin-rotation matrix determined from the numerical solution of the BHZ model with Rashba SOI using Eq. (13).