Brillouin-Wigner theory for Floquet topological phase transitions in spin-orbit-coupled materials

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(ω⁻¹) but by keeping all the important terms to order O(ω⁻²) and obtain the photoassisted correction terms to both the hopping and the spin-orbit terms, as well as 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.