Localization and mobility edges in non-Hermitian continuous quasiperiodic systems

TL;DR

This paper explores the localization transition and mobility edges in a one-dimensional non-Hermitian quasiperiodic continuous system, revealing unique spectral topology and critical behavior linked to the non-Hermitian skin effect.

Contribution

It introduces the first analysis of mobility edges and localization in a non-Hermitian continuum quasiperiodic system, highlighting spectral topology and critical phenomena.

Findings

Mobility edge located in the real spectrum between localized and extended states.

Open energy spectrum with high-energy extended states characterized by a non-zero winding number.

Critical potential amplitude with a universal exponent approximately 1/3.

Abstract

The mobility edge (ME) is a fundamental concept in the Anderson localized systems, which marks the energy separating extended and localized states. Although the ME and localization phenomena have been extensively studied in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we investigate the ME and localization properties of a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schr{\"o}dinger equation with an imaginary vector potential and an incommensurable one-site potential. We find that the ME is located in the real spectrum and falls between the localized and extended states. Additionally, we show that under the periodic boundary condition, the energy spectrum always exhibits an open curve representing high-energy extended electronic states characterized by a non-zero integer winding number. This complex spectrum topology is closely connected with the non-Hermitian skin effect (NHSE) observed under open boundary conditions, where the eigenstates of the bulk bands accumulate at the boundaries. Furthermore, we analyze the critical behavior of the localization transition and obtain critical potential amplitude accompanied by the universal critical exponent $\nu \simeq 1/3$. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.