Chiral Flow in One-dimensional Floquet Topological Insulators

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.