Probing Floquet topological phases via non-Hermitian skin effect of reflected waves

TL;DR

This paper explores how the non-Hermitian skin effect manifests in reflected waves of Floquet topological phases, linking scattering properties to topological invariants in driven systems.

Contribution

It introduces a scattering formalism connecting the non-Hermitian winding number of reflection matrices to Floquet topological invariants, revealing a gap-dependent GH shift.

Findings

Reflected-wave NHSE depends on quasienergy gap.

Momentum-integrated GH shift quantifies Floquet topological invariant.

Frequency-dependent NHSE observed in driven systems.

Abstract

Periodically driven systems host topological phases without static analogs, such as the anomalous Floquet phase characterized by trivial bulk bands yet robust boundary modes. In this work, we investigate the scattering problem of a Floquet Chern insulator and reveal the non-Hermitian skin effect (NHSE) of reflected waves. Using a discrete-time scattering formalism, we demonstrate how the non-Hermitian winding number of the reflection matrix is linked to the bulk Floquet invariant via boundary resonances. This reflected-wave NHSE relies on which quasienergy gap the incident wave resides in, leading to a gap-dependent Goos-H\"anchen (GH) shift. We further show that the momentum-integrated GH shift quantitatively yields the Floquet topological invariant of the corresponding gap. Our work highlights a frequency-dependent NHSE of reflected waves in driven systems and provides a real-space scattering approach to identify non-equilibrium topology.