Backscattering off a driven Rashba impurity at the helical edge

TL;DR

This paper investigates how a periodically driven Rashba impurity affects electron backscattering at the edges of topological insulators, revealing non-monotonic frequency dependence linked to electron interactions.

Contribution

It introduces a perturbative analysis of a driven Rashba impurity's impact on helical edge transport, highlighting a unique non-monotonic frequency response.

Findings

Backscattering current is non-monotonic in driving frequency.

Non-monotonicity is specific to Rashba impurities, not magnetic ones.

The behavior directly relates to the Luttinger parameter K.

Abstract

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 only visible 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 non-monotonic 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 non-monotonic behaviour allows us to directly link the backscattering current to the Luttinger parameter $K$, encoding the strength of electron-electron interactions.