Topological Floquet bands in a circularly shaken dice lattice

Abstract

The hoppings of noninteracting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasienergy bands in the quasienergy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasienergy band shows that when the hopping strengths of the nearest-neighbor hoppings are isotropic, the system persists in the topologically nontrivial phases with Chern number C=2 within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighbor hopping strengths, a topological phase transition occurs, making the Chern number change from C=2 to C=1. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the nontrivially topological characteristics of optical dice lattices by applying periodic shaking and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.