Floquet states of $ α$-$T_3$ lattice: Role of variable Berry phase

Bashab Dey, Tarun Kanti Ghosh

Published 2018-05-28Version 1

We consider $\alpha$-$T_3$ model illuminated by intense circularly polarized radiation in terahertz regime. We present quasienergy band structure, time-averaged energy spectrum and time-averaged density of states of $\alpha$-$T_3$ model by solving the Floquet Hamiltonian. 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 $\alpha$. Approximate forms of quasienergy and band gaps at single and multi-photon resonant points are derived using rotating wave approximation. The expressions reveal a stark dependence of quasienergy on the Berry phase of the charge carrier. The quasi energy flat band remains unchanged in presence of radiation for dice lattice. 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 also broken for $0<\alpha<1$. Unlike graphene, the mean energy follows closely the linear dispersion of Dirac cones till near the two-photon resonant points. There are additional peaks in the time-averaged density of states at the Dirac point for $0<\alpha \leq 1$.