Topological Floquet-bands in a circularly shaken dice lattice

TL;DR

This paper demonstrates how periodic shaking of an optical dice lattice induces topological Floquet bands with tunable Chern numbers, revealing topological phase transitions driven by anisotropic hopping strengths.

Contribution

It introduces a method to realize and control topological phases in optical dice lattices through periodic shaking, including analytical verification of phase transitions.

Findings

Periodic driving creates gapped Floquet bands with non-trivial topology.

Isotropic hopping maintains a Chern number of 2 over a wide range of driving.

Anisotropic hopping induces a topological phase transition from C=2 to C=1.

Abstract

The hoppings of non-interacting 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 quasi-energy bands in the quasi-energy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasi-energy band shows that when the hopping strengths of the nearest-neighboring hoppings are isotropic, the system persists in the topologically non-trivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighboring hopping strengths, a topological phase transition occurs, making 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 non-trivially topological characteristics of optical dice lattices by applying the periodic shaking, and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.