Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application elliptically polarized light. In particular, we analyze Bernevig-Hughes-Zhang model when it is perturbed using an light frequency $\mathrm{\ensuremath{\Omega}}$ described in general vector potential $\mathbf{A}(t)=({A}_{0x}cos(\mathrm{\ensuremath{\Omega}}t),{A}_{0y}cos(\mathrm{\ensuremath{\Omega}}t+{\ensuremath{\phi}}_{0}))$. Even for fixed value ${\ensuremath{\phi}}_{0}$, can change character changing $x$ and $y$ amplitudes drive. therefore find rich phase diagram as function ${A}_{0x}$, ${A}_{0y}$, ${\ensuremath{\phi}}_{0}$. each these phases, invariant given Chern number consistent with spin-polarized states present at edges nanoribbon.