Floquet topological phase transition in the α-T3 lattice

We investigate topological characteristics of the photon-dressed band structure of the alpha-T-3 lattice on being driven by off-resonant circularly polarized radiation. We obtain exact analytical expressions of the quasienergy bands over the first Brillouin zone. The broken time-reversal symmetry caused by the circularly polarized light lifts the triple point degeneracy completely at both the Dirac points. The gaps become unequal at K and K' (except at alpha = 0 and 1), which reveals the absence of inversion symmetry in the system. At alpha = 1/root 2, the gap between the flat and valence bands closes at K, while that between the conduction and flat bands closes at K', thereby restoring a semimetalic phase. At the gap closing point (alpha = 1/root 2) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around K and K' points. Under the influence of the circularly polarized radiation, the alpha-T-3 lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by nonzero Chern number. The system undergoes a topological phase transition from C = 1( -1 ) to C = 2( -2) at alpha = 1/root 2, where C is the Chern number of the valence (conduction) band. This sets an example of a multiband system having larger Chern number. These results are supported by the appearance of chiral edge states in an irradiated alpha-T-3 nanoribbon.