Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk

TL;DR

This paper reveals that anomalous Floquet topological insulators can induce a boundary non-Hermitian skin effect due to their bulk topology, connecting periodically-driven systems with non-Hermitian physics and offering new ways to generate skin effects.

Contribution

It introduces a new form of 'mixed' higher-order topology where Floquet bulk topology causes boundary non-Hermitian skin effects, bridging driven systems and non-Hermitian phenomena.

Findings

Boundary non-Hermitian skin effect occurs in anomalous Floquet topological insulators.

Removing a boundary hopping halts chiral edge mode propagation.

Bulk Floquet topology is linked to boundary skin effects via a real-space invariant.

Abstract

We show that anomalous Floquet topological insulators generate intrinsic, non-Hermitian topology on their boundary. As a consequence, removing a boundary hopping from the time-evolution operator stops the propagation of chiral edge modes, leading to a non-Hermitian skin effect. This does not occur in Floquet Chern insulators, however, in which boundary modes continue propagating. The non-Hermitian skin effect on the boundary is a consequence of the nontrivial topology of the bulk Floquet operator, which we show by designing a real-space topological invariant. Our work introduces a form of `mixed' higher-order topology, providing a bridge between research on periodically-driven systems and the study of non-Hermiticity. It suggests that periodic driving, which has already been demonstrated in a wide range of experiments, may be used to generate non-Hermitian skin effects.