Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model

TL;DR

This paper demonstrates how to control and reverse the state of a classical spin coupled to the helical edge states of a Kane-Mele model by manipulating spin-polarization clouds, enabling precise spin state steering.

Contribution

It introduces a method to control and reverse a classical spin via injection and scattering of spin-polarization clouds in a topological insulator edge system.

Findings

Single process effects can be largely reversed with subsequent processes.

Concatenated processes enable complete spin state switching.

Full spin reversal is achievable through controlled injection and scattering.

Abstract

The time-dependent state of a classical spin locally exchange coupled to an edge site of a Kane-Mele model in the topologically non-trivial phase is studied numerically by solving the full set of coupled microscopic equations of motion for the spin and the electron system. Dynamics in the long-time limit is accessible thanks to dissipative boundary conditions, applied to all but the zigzag edge of interest. We study means to control the state of the spin via transport of a spin-polarization cloud through the helical edge states. The cloud is formed at a distant edge site using a local magnetic field to inject an electron spin density and released by suddenly switching off the injection field. This basic process, consisting of spin injection, propagation of the spin-polarization cloud, and scattering of the cloud from the classical spin, can be used to steer the spin state in a controlled way. We find that the effect of a single basic process can be reverted to a high degree with a subsequent process. Furthermore, we show that by concatenating several basic injection-propagation-scattering processes, the spin state can be switched completely and that a full reversal can be achieved.