Exact mobility edges and topological phase transition in two-dimensional non-Hermitian quasicrystals

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