Localization and mobility edges in non-Hermitian continuous quasiperiodic systems

Abstract

The mobility edge (ME) is a critical concept in Anderson localized systems, which marks the boundary between extended and localized states. Although the ME and localization phenomena have been extensively investigated in non-Hermitian (NH) quasiperiodic tight-binding models, they remain limited to NH continuum systems. Here, we study the ME and localization behaviors in a one-dimensional (1D) NH quasiperiodic continuous system, which is described by a Schrödinger equation with an incommensurable one-site potential and an imaginary vector 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 eigenstates 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. We also analyze the critical behavior of the localization transition and obtain the critical potential strength accompanied by the critical exponent $\nu \simeq 1/3$ . Furthermore, we investigate the expansion dynamics to dynamically probe the existence of NHSE and MEs, and outline a possible experimental implementation. Our study provides valuable inspiration for exploring MEs and localization behaviors in NH quasiperiodic continuous systems.

Keywords

• Anderson transition
• mobility edge
• non-Hermitian quasicrystal
• continuous systems