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


الملخص بالإنكليزية

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 picture promotes discovering of models with the exact MEs in lower-dimensional systems. While most of previous studies concern on the one-dimensional (1D) quasiperiodic systems, the analytic results that allow for an accurate understanding of two-dimensional (2D) cases are rare. In this Letter, 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 of topological nature characterized by a hidden winding number defined in the dual space. The 2D non-Hermitian quasicrystal model can be realized in the coupling waveguide platform, and the localization features can be detected by the excitation dynamics.

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