Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals

Longwen Zhou

doi:10.1103/physrevresearch.3.033184

Abstract

Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.

Highlights

Floquet engineering has enabled the realization of rich dynamical, topological, and transport phenomena in a broad range of physical settings [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
It was found that the interplay between time-periodic driving fields and gain and loss or nonreciprocal effects could yield topological phases that are unique to non-Hermitian Floquet systems [43,44,45,46,47,48,49,50]
The conditions of localization transition for these models have been derived in previous studies

Summary

Introduction

Floquet engineering has enabled the realization of rich dynamical, topological, and transport phenomena in a broad range of physical settings [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. It was found that the interplay between time-periodic driving fields and gain and loss or nonreciprocal effects could yield topological phases that are unique to non-Hermitian Floquet systems [43,44,45,46,47,48,49,50]. These intriguing phases are characterized by large integer or half-integer winding numbers and degenerate Floquet edge or corner states with real quasienergies [43,44,45,46,47,48,49]. Much less is known when non-Hermitian Floquet systems are subject to more complicated correlation effects, such as disorder, nonlinearity, and many-body interactions

Methods

Results

Conclusion