  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.
