Photoinduced valley and electron-hole symmetry breaking in α-T3 lattice: The role of a variable Berry phase

We consider an alpha-T-3 lattice illuminated by intense circularly polarized radiation in the terahertz regime. We present the quasienergy band structure, time-averaged energy spectrum, and time-averaged density of states of an alpha-T-3 lattice by solving the Floquet Hamiltonian numerically. We obtain exact analytical expressions of the quasienergies at the Dirac points for all values of alpha and field strength. We find that the quasienergy band gaps at the Dirac point decrease with increase of a. Approximate forms of quasienergy and band gaps at single- and multiphoton resonant points are derived using the rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasienergy flat band remains unaltered in the presence of radiation for a dice lattice (alpha = 1). However, it acquires a dispersion in and around the Dirac and even-photon resonant points when 0 < alpha < 1. The valley degeneracy and electron-hole symmetry in the quasienergy spectrum are broken for 0 < alpha < 1. Unlike graphene, the mean energy closely follows the linear dispersion of the Dirac cones until near the single-photon resonant point in the dice lattice. There are additional peaks in the time-averaged density of states at the Dirac point for 0 < alpha <= 1.