Bandwidth-resonant Floquet states in honeycomb optical lattices

TL;DR

This paper explores topological phases in a shaken honeycomb optical lattice using Floquet theory, revealing how intermediate shaking frequencies induce band overlaps and resonances that lead to novel out-of-equilibrium topological states.

Contribution

It demonstrates that two-phonon resonances in a shaken honeycomb lattice can produce topological phases describable by the BHZ model, linking out-of-equilibrium phenomena to known topological insulators.

Findings

Identification of topological phases arising from Floquet band overlaps

Two-phonon resonances induce topological states similar to HgTe quantum wells

Band inversions explain out-of-equilibrium topological phenomena

Abstract

We investigate, within Floquet theory, topological phases in the out-of-equilibrium system that consists of fermions in a circularly shaken honeycomb optical lattice. We concentrate on the intermediate regime, in which the shaking frequency is of the same order of magnitude as the band width, such that adjacent Floquet bands start to overlap, creating a hierarchy of band inversions. It is shown that two-phonon resonances provide a topological phase that can be described within the Bernevig-Hughes-Zhang model of HgTe quantum wells. This allows for an understanding of out-of-equilibrium topological phases in terms of simple band inversions, similar to equilibrium systems.