Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic 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.

arXiv comment10 pages, 4 figures, submitted to Physical Review A

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• Atomic quantum gases in periodically driven optical lattices
• Topological Bands for Ultracold Atoms
• Floquet Topological Phases of Non-Hermitian Systems
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Floquet analysis of a quantum system with modulated periodic driving
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• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term