Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials

TL;DR

This paper develops a high frequency expansion using Brillouin-Wigner perturbation theory to analyze Floquet topological phase transitions in spin-orbit coupled materials like silicene, germanene, and stanene, providing accurate effective Hamiltonians.

Contribution

It introduces a detailed high frequency expansion method for driven spin-orbit coupled systems, including higher-order corrections and longer ranged hopping terms.

Findings

High frequency expansion accurately predicts Floquet topological phases.

Effective Hamiltonian includes photo-assisted and longer ranged hopping terms.

The theory matches numerical Chern number calculations at large frequencies.

Abstract

We develop the high frequency expansion based on the Brillouin-Wigner (B-W) perturbation theory for driven systems with spin-orbit coupling which is applicable to the cases of silicene, germanene and stanene. We compute the effective Hamiltonian in the zero photon subspace not only to order $O(\omega^{-1})$, but by keeping all the important terms to order $O(\omega^{-2})$, and obtain the photo-assisted correction terms to both the hopping and the spin-orbit terms, as well as new longer ranged hopping terms. We then use the effective static Hamiltonian to compute the phase diagram in the high frequency limit and compare it with the results of direct numerical computation of the Chern numbers of the Floquet bands, and show that at sufficiently large frequencies, the B-W theory high frequency expansion works well even in the presence of spin-orbit coupling terms.