One-dimensional driven non-Hermitian quasicrystals

Abstract

The phenomenon of localization of matter waves in condensed matter systems has been ubiquitous ever since its inception over sixty years ago. In this work, we study the delocalization-localization (DL) transition in non-equilibrium driven systems comprising of the static Hermitian and non-Hermitian (asymmetric) Aubry-Andr ́e-Harper (AAH) Hamiltonians on either realms of the drive. It is observed that one of the driven systems (with Hermiticity on the earlier realm of the drive) does not undergo the DL transition, unlike the static constituents. We have found evidences that such a driven system demonstrates a multifractal regime for a wide range of the quasiperiodic potential, which is absent in the static quasicrystals of AAH type. Furthermore, the latter devised driven system (with non- Hermiticity on both realms of the drive) exhibits skin-effect and the states localize at a boundary depending upon the condition of the ultimate drive. To our mind, these unique localization features in the driven systems might be beneficial to experimentalists working in cold-atoms