Backscattering off a driven Rashba impur

The spin degree of freedom is crucial for both understanding and exploiting the particular properties of the edges of two-dimensional topological insulators. In this context, we analyze the effects of a periodically driven Rashba impurity at the helical edge in the presence of electron-electron interactions. By treating these interactions using bosonization techniques, we compute the backscattering current perturbatively up to second order in the impurity strength. Our results reveal that the backscattering current demonstrates a nonmonotonic dependence on the driving frequency. This feature is a unique signature of the Rashba impurity, which is not present in cases involving magnetic impurities in the helical liquid. Furthermore, this nonmonotonic behavior allows us to establish a direct connection between the backscattering current and the Luttinger parameter K, which encapsulates the strength of electron-electron interactions. Our findings contribute to the understanding of transport properties in helical edge states and have implications for potential applications in spintronics and quantum information technologies.