Backscattering off a driven Rashba impurity at the helical edge

The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In the absence of superconductivity and magnetism, Rashba coupling is the most relevant single-particle perturbation in this system. Since Rashba coupling does not break time reversal symmetry, its influence on transport properties is visible only if processes that do not conserve the single-particle energy are included. Paradigmatic examples of such processes are electron-electron interactions and time-dependent external drivings. We analyze the effects of a periodically driven Rashba impurity at the helical edge, in the presence of electron-electron interactions. Interactions are treated by means of bosonization, and the backscattering current is computed perturbatively up to second order in the impurity strength. We show that the backscattering current is nonmonotonic in the driving frequency. This property is a fingerprint of the Rashba impurity, being absent in the case of a magnetic impurity in the helical liquid. Moreover, the nonmonotonic behavior allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions.

Figure 1

Zoom around $\omega ={\omega }_0$ of $\langle {\widehat{I}}_{BS}^{\mathrm{dc}}\rangle$, measured in units of $[e{\alpha }_0^2{k}_F^2{\left(k_{F}a\right)}^{\left(2K\right)}/\left({\hslash }^2{\omega }_0\right)]$ for $K=0.8$ (violet), $K=0.7$ (green), and $K=0.6$ (red). We further set $\hslash =1$ and $E_F=0.1\hslash {\omega }_0$.

Figure 2

The relative jump defined in the text as a function of the interaction parameter $K$.