Dynamic impurities in two-dimensional topological insulator edge states

Two-dimensional topological insulators host one-dimensional helical states at the edges.
These are characterized by spin-momentum locking and time-reversal symmetry protects the states from backscattering by potential impurities.
Magnetic impurities break time-reversal symmetry and allow for backscattering.
In an earlier work we investigated the effects of random, static, aligned magnetic impurities [1] on the spectrum and found that for fixed magnetic impurity strength the gap in the density of states (DOS) closes with rising potential strength.

We are now moving on to investigate the effect of random, aligned but harmonically rotating magnetic impurities.
Using the time dependent Green’s function (GF) for the system we calculate the time-averaged DOS.
For slow driving the DOS matches an average over static impurity orientations, whereas fast driving results in a flat low-energy DOS with resonances at higher energies related to Floquet sub-band crossings and resonant driving leads to a nontrivial DOS.
A Fourier representation of the GF also gives access to transport properties of the system.

[1] S. Wozny, K. Vyborny, W. Belzig, and S. I. Erlingsson, "Gap formation in helical edge states with magnetic impurities", Phys. Rev.
B 98, 165423 (2018)