Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state

TL;DR

This paper presents a scheme to realize Floquet topological bands with ultracold atoms in a shaken optical lattice, exploring how induced interactions affect the stability of a bosonic fractional Chern insulator state.

Contribution

It introduces a method to create topological quasienergy bands in a driven optical lattice and analyzes the effects of interaction-induced terms on fractional Chern insulator stability.

Findings

Topological band gap is opened via Floquet engineering with lattice shaking.

Interaction terms include nearest neighbor density interactions and density-assisted tunneling.

Induced interactions influence the stability of the fractional Chern insulator state.

Abstract

We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice that lowers the energy on every other site. The topological band gap, which separates the two bands with Chern numbers $\pm 1$, is opened in a way characteristic to Floquet topological insulators, namely, by terms of the effective Hamiltonian that appear in subleading order of a high-frequency expansion. These terms correspond to processes where a particle tunnels several times during one driving period. The interplay of such processes with particle interactions also gives rise to new interaction terms of several distinct types. For bosonic atoms with on-site interactions, they include nearest neighbor density-density interactions introduced at the cost of weakened on-site repulsion as well as density-assisted tunneling. Using exact diagonalization, we investigate the impact of the individual induced interaction terms on the stability of a bosonic fractional Chern insulator state at half filling of the lowest band.