Counter-propagating edge modes and topological phases of a kicked quantum Hall system

TL;DR

This paper investigates a periodically driven quantum Hall system revealing anomalous counter-propagating edge modes protected by symmetry, which differ from stationary systems and are robust against disorder, highlighting new topological phases.

Contribution

It introduces a new class of topological phases with counter-propagating edge modes in driven quantum Hall systems, emphasizing the role of symmetry in their protection and classification.

Findings

Discovery of anomalous edge modes with opposite chirality

Edge modes are protected by chiral symmetry and robust against disorder

Identification of phases with identical Chern numbers but different edge spectra

Abstract

A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the "wrong" chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.