Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems

Abstract

The presence of disorder can severely impede wave transport, resulting in the famous Anderson localization. Previous theoretical studies found that Anderson transition can exist in one-dimensional (1D) non-Hermitian disordered rings with chiral hopping, defying the scaling theory of localization for Hermitian systems. In these systems, localized (extended) modes are associated with real (complex) energies. Here, we report that Anderson localized modes with complex energies can also exist in such systems. The emergence of the complex-energy localized modes (CELMs) directly ties to the properties of the corresponding pristine non-Hermitian system. Specifically, the density of states of the complex spectrum under the periodic boundary condition and the non-Bloch parity-time transition of the open-boundary chain both play critical roles in the emergence of the CELMs. The coexistence of extended modes, real-energy localized modes (RELMs), and CELMs should be a generic phenomenon for 1D non-Hermitian disordered systems under class AI. Our work shows that the interplay between Anderson mechanism and non-Hermitian physics enriches the properties of disordered media and opens new possibilities for controlling wave transport.

16 pages, 5 figures

References in corpus (30)

• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Localization of ultrasound in a three-dimensional elastic network
• Non-Hermitian Topology and Exceptional-Point Geometries
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Non-Hermitian topological phenomena: A review
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Topological Non-Hermitian skin effect
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian Morphing of Topological Modes
• Observation of non-Bloch parity-time symmetry and exceptional points
• Non-Hermitean Random Matrix Theory: method of hermitization
• Non-Hermitean Localization and De-Localization
• Universality classes of non-Hermitian random matrices
• Geometric Origin of Non-Bloch PT Symmetry Breaking
• Non-Hermitean De-Localization: Multiple Scattering and Bounds
• Topology in non-Hermitian Chern insulators with skin effect
• Extended topological mode in a one-dimensional non-Hermitian acoustic crystal
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms

Cited by in corpus (8)

• Universal non-Hermitian transport in disordered systems
• Mobility rings in a non-Hermitian non-Abelian quasiperiodic lattice
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Exceptional deficiency of non-Hermitian systems
• Experimental Realization of Special-Unitary Operations in Classical Mechanics by Nonadiabatic Evolutions
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Recent progress on disorder-induced topological phases
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain