Dynamic Friedel oscillations on the surface of a topological insulator

We study theoretically the dynamic Friedel oscillations of electrons at the surface of a topological insulator (TI) that are generated by the rotation of a localized impurity spin. We show that the spin-orbit interaction (SOI) in Rashba form, which is an integral part of the TI Hamiltonian, yields a highly anisotropic response to the localized spin rotation. As a result, the response to a flip of a localized spin $z$ projection involves the reaction of all $x$, $y$, and $z$ components of the local magnetization. Additionally, the dynamic spin moment (and thus also Friedel oscillations) emitted by the localized dynamical spin depends on the orientation in the TI plane. The resulting unusual dynamics is due to the interplay of SOI and Ruderman-Kittel-Kasuya-Yoshida interactions. This provides the basis for manipulation of the spin transport in topological insulators decorated with localized impurity spins, which may be important for technological applications.