Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals

TL;DR

This paper introduces an exactly solvable 2D non-Hermitian quasicrystal model with parity-time symmetry, revealing precise mobility edges and a topological phase transition characterized by a hidden winding number, with potential experimental realization in waveguide systems.

Contribution

It provides the first exact 2D model with mobility edges and topological transition, advancing understanding of non-Hermitian quasicrystals beyond 1D.

Findings

Exact mobility edges in a 2D non-Hermitian quasicrystal

Topological characterization of the phase transition via a hidden winding number

Potential realization in waveguide experiments

Abstract

The emergence of the mobility edge (ME) has been recognized as an important characteristic of Anderson localization. The difficulty in understanding the physics of the MEs in three-dimensional (3D) systems from a microscopic image encourages the development of models in lower-dimensional systems that have exact MEs. While most of the previous studies are concerned with one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this work, we disclose an exactly solvable 2D quasicrystal model with parity-time ($\mathcal{PT}$) symmetry displaying exact MEs. In the thermodynamic limit, we unveil that the extended-localized transition point, observed at the $\mathcal{PT}$ symmetry breaking point, is topologically characterized by a hidden winding number defined in the dual space. The coupling waveguide platform can be used to realize the 2D non-Hermitian quasicrystal model, and the excitation dynamics can be used to detect the localization features.