Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems

TL;DR

This paper explores the unique topological properties of periodically-driven 2D systems, revealing anomalous edge states not explained by traditional invariants, and introduces a new topological invariant to characterize these phenomena.

Contribution

The authors develop a new topological invariant for driven 2D systems that accurately predicts edge states, distinguishing them from static system topologies.

Findings

Robust chiral edge states can exist without non-zero Chern numbers.

A new topological invariant explains anomalous edge states in driven systems.

Formulations in time and frequency domains provide insight into Floquet spectra.

Abstract

Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed that the topological characterization of driven systems is richer than that of static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the "anomalous" spectra which arise in driven systems. Possible realizations of these phenomena in solid state and cold atomic systems are discussed.