Charge density wave and charge pump of interacting fermions in circularly shaken hexagonal optical lattices

TL;DR

This paper investigates the effects of strong correlations and topological properties of interacting fermions in circularly shaken hexagonal optical lattices, revealing how interactions influence charge density waves, edge states, and charge pumping, with implications for experimental measurements.

Contribution

It introduces a real-space Floquet DMFT approach to analyze topological and correlation effects in the Haldane-Falicov-Kimball model within shaken optical lattices, and proposes an experimental protocol for quantized charge pumping.

Findings

Interactions induce charge density waves affected by resonant tunneling.

Interactions cause edge state smearing and finite quasiparticle lifetime.

Pumped charge is non-integer due to dissipation effects, even at low temperatures.

Abstract

We analyze strong correlation effects and topological properties of interacting fermions with a Falicov-Kimball type interaction in circularly shaken hexagonal optical lattices, which can be effectively described by the Haldane-Falicov-Kimball model, using the real-space Floquet dynamical mean-field theory (DMFT). The Haldane model, a paradigmatic model of the Chern insulator, is experimentally relevant, because it has been realized using circularly shaken hexagonal optical lattices. We show that in the presence of staggering a charge density wave emerges, which is affected by interactions and resonant tunneling. We demonstrate that interactions smear out the edge states by introducing a finite life time of quasiparticles. Even though a general method for calculating the topological invariant of a nonequilibrium steady state is lacking, we extract the topological invariant using a Laughlin charge pump set-up. We find and attribute to the dissipations into the bath connected to every lattice site, which is intrinsic to real-space Floquet DMFT methods, that the pumped charge is not an integer even for the non-interacting case at very low reservoir temperatures. Furthermore, using the rate equation based on the Floquet-Born-Markov approximation, we calculate the charge pump from the rate equations for the non-interacting case to identify the role of the spectral properties of the bath. Starting from this approach we propose an experimental protocol for measuring quantized charge pumping.