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

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 ($\mathcal{P}\mathcal{T}$) symmetry displaying exact MEs. In the thermodynamic limit, we unveil that the extended-localized transition point, observed at the $\mathcal{P}\mathcal{T}$ 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.

9 pages, 7 figures

References in corpus (16)

• Making Sense of Non-Hermitian Hamiltonians
• Anderson Transitions
• Localization of ultrasound in a three-dimensional elastic network
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological phase transition in non-Hermitian quasicrystals
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Experimental observation of strong photon localization in disordered photonic crystal waveguides
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

Cited by in corpus (19)

• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Anti-parity-time symmetry hidden in a damping linear resonator
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model
• Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Equivalence and superposition of real and imaginary quasiperiodicities
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Unconventional superfluidity of superconductivity on Penrose lattice
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals