Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice

Abstract

We investigate topological characteristics of the photon-dressed band structure of $\alpha$-${\mathcal{T}}_3$ 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 $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ (except at $\alpha =0$ and 1), which reveals the absence of inversion symmetry in the system. At $\alpha =1/\sqrt{2}$, the gap between flat and valence bands closes at $\mathbf{K}$, while that between conduction and flat bands closes at ${\mathbf{K}}^{\prime }$, thereby restoring a semimetalic phase. At the gap closing point ($\alpha =1/\sqrt{2}$) which is independent of the radiation amplitude, there is a reappearance of low-energy Dirac cones around $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points. Under the influence of the circularly polarized radiation, the $\alpha$-${\mathcal{T}}_3$ lattice is transformed from semimetal to a Haldane-like Chern insulator characterized by non-zero Chern number. The system undergoes a topological phase transition from $\mathcal{C}=1(-1)$ to $\mathcal{C}=2(-2)$ at $\alpha =1/\sqrt{2}$, where $\mathcal{C}$ 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 irradiated $\alpha$-${\mathcal{T}}_3$ nanoribbon.

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Cited by in corpus (1)

• Dynamical Floquet spectrum of Kekulé-distorted graphene under normal incidence of electromagnetic radiation