Quantum tunneling in the dice lattice irradiated with circularly polarized light

We investigate the properties of quantum tunneling across a smooth square electrostatic potential barrier in the dice model irradiated with circularly polarized light. The resulting time-dependent Hamiltonian is reduced to an effective Hamiltonian with the use of the Floquet-Magnus high-frequency expansion valid off-resonance. The flat band is located at the center of the bandgap band and is not affected by irradiation. The linear dispersion in the dice model is modified in the presence of the irradiation, leading to the destruction of the Klein tunneling for normal incidence. It is demonstrated that the additional irradiation term, in general, suppresses the transmission. We investigate the conditions for super-Klein tunneling when there is perfect transmission over a wide angle of incidence. We also report our results for the ballistic conductance as the energy gap is modified by the irradiation.