Manipulating Floquet-driven topological insulator with off-resonant elliptically polarized light in presence of hexagonal Fermi surface warping

The irradiation of topological insulator surface with elliptically polarized light modifies the topological properties in a phase-dependent manner impacting the Floquet Chern number which is a crucial topological invariant associated with such driven systems. Employing Floquet theory in presence of hexagonal warping term in the Dirac fermion Hamiltonian under off-resonant conditions, we derive an effective Hamiltonian that highlights distinct features in the Floquet-Dirac surface states. Specifically, we identify a helicity and ellipticity-dependent mass term in the quasi-static Hamiltonian, breaking time reversal symmetry. This mass term changes sign with variations in the helicity and ellipticity of incident radiation, potentially driving the system into trivial or Floquet-Chern topological insulating phases. We calculate the Berry curvature associated with the bandstructure and the resulting anomalous Hall conductivity, finding a strong dependence on the ellipticity and amplitude of the radiation.