$q$th-root non-Hermitian Floquet topological insulators

TL;DR

This paper introduces a method to generate fractional quasienergy topological insulators by taking the $q$th-root of Floquet evolution operators, revealing controllable edge and corner modes in non-Hermitian Floquet systems.

Contribution

It presents a novel $q$th-root procedure for Floquet operators, enabling the construction of fractional quasienergy topological phases in non-Hermitian Floquet insulators.

Findings

Multiple fractional quasienergy edge and corner modes identified.

Non-Hermiticity induces fractional-quasienergy corner modes.

Coexistence of non-Hermitian skin effect with fractional quasienergy states.

Abstract

Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer $q$th-root of the evolution operator $U$ that describes Floquet topological matter. We further apply our $q$th-rooting procedure to obtain $2^n$th- and $3^n$th-root first- and second-order non-Hermitian Floquet topological insulators (FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies $\pm(0,1,...2^{n})\pi/2^{n}$ and $\pm(0,1,...,3^{n})\pi/3^{n}$, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.