Chiral Flow in One-dimensional Floquet Topological Insulators

TL;DR

This paper introduces a new bulk topological invariant called chiral flow for one-dimensional Floquet topological insulators with chiral symmetry, which accurately characterizes particle transport and edge modes even in disordered systems.

Contribution

It develops a physically motivated, locally computable topological invariant for Floquet systems with chiral symmetry, extending topological classification to disordered cases and establishing a bulk-edge correspondence.

Findings

Defines the chiral flow invariant for Floquet systems

Establishes a bulk-edge correspondence relating chiral flow to edge modes

Introduces real-space edge invariants for dynamical boundary classification

Abstract

We propose a bulk topological invariant for one-dimensional Floquet systems with chiral symmetry which quantifies the particle transport on each sublattice during the evolution. This chiral flow is physically motivated, locally computable, and improves on existing topological invariants by being applicable to systems with disorder. We derive a bulk-edge correspondence which relates the chiral flow to the number of protected dynamical edge modes present on a boundary at the end of the evolution. In the process, we introduce two real-space edge invariants which classify the dynamical topological boundary behavior at various points during the evolution. Our results provide the first explicit bulk-boundary correspondence for Floquet systems in this symmetry class.