Absence of Wannier-Stark Localization and Skin Effect in Driven Non-Hermitian Systems

Abstract

Since long, it is theorized that the electronic eigenstates become completely localized in the presence of an external electric field, manifesting equally spaced energies, known as the Wannier-Stark (WS) localization. The localization behavior also persists in non-Hermitian Hamiltonians, and when the system is governed by a quasiperiodic potential. In this work, we have explored different phases by identifying the delocalization-localization (DL) phase transition in such non-Hermitian quasicrystals in the presence of a time-periodic external electric field. In stark contrast to the static counterparts where the states can either be completely delocalized or localized, we demonstrate that under the time-periodic drive there exists multiple mobility edges separating the metallic and insulating states when the electric field is driven slowly. We find that a time-periodicity introduced in the electric field significantly amplifies the regime of delocalized eigenstates upto an enhanced strength of the quasiperiodic potential, which is analytically verified in the regime of a large driving frequency. We find that the well-known WS energy ladders inherent in the systems with an uniform electric field no longer prevail in the periodically driven framework, and the energy levels exhibit the Poissonian statistics when the eigenstates are localized. Finally, we stress that the extended unitarity leads to the destruction of skin effect, which prevails only beyond some critical value of the non-Hermiticity in the Hamiltonian and is dependent upon the strength of the time-modulated electric field.