Driving-induced multiple PT -symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals

Abstract

The cooperation between time-periodic driving fields and non-Hermitian effects could endow systems with distinctive spectral and transport properties. In this paper, we uncover an intriguing class of non-Hermitian Floquet matter in one-dimensional quasicrystals, which is characterized by the emergence of multiple driving-induced $\mathcal{PT}$-symmetry breaking/restoring transitions, mobility edges, and reentrant localization transitions. These findings are demonstrated by investigating the spectra, level statistics, inverse participation ratios, and wave-packet dynamics of a periodically quenched nonreciprocal Harper model. Our results not only unveil the richness of localization phenomena in driven non-Hermitian quasicrystals but also highlight the advantage of the Floquet approach in generating unique types of nonequilibrium phases in open systems.