Floquet second-order topological insulators in non-Hermitian systems

TL;DR

This paper demonstrates how periodic driving can induce and control exotic non-Hermitian second-order topological insulators with tunable boundary states in 2D and 3D systems, overcoming non-Hermitian bulk-boundary correspondence issues.

Contribution

It introduces a scheme to realize and describe non-Hermitian SOTIs via bulk topology in nonequilibrium systems with periodic driving.

Findings

Rich non-Hermitian SOTIs with tunable corner and hinge states

Recovery of bulk-boundary correspondence in non-Hermitian systems

Coexistence of first- and second-order topological phases

Abstract

Second-order topological insulator (SOTI) is featured with the presence of $(d-2)$-dimensional boundary states in $d$-dimension systems. The non-Hermiticity induced breakdown of bulk-boundary correspondence (BBC) and the periodic driving on systems generally obscure the description of non-Hermitian SOTI. To prompt the applications of SOTIs, we explore the role of periodic driving in controllably creating exotic non-Hermitian SOTIs both for 2D and 3D systems. A scheme to retrieve the BBC and a complete description to SOTIs via the bulk topology of such nonequilibrium systems are proposed. It is found that rich exotic non-Hermitian SOTIs with a widely tunable number of 2D corner states and 3D hinge states and a coexistence of the first- and second-order topological insulators are induced by the periodic driving. Enriching the family of topological phases, our result may inspire the exploration to apply SOTIs via tuning the number of corner/hinge states by the periodic driving.