Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension

Abstract

Symmetry-protected spectral topology in non-Hermitian systems has interesting manifestations such as dynamically anomalous chiral currents and skin effect. We study the interplay between symmetries and disorder in a paradigmatic model for spectral topology - the non-reciprocal Su-Schrieffer-Heeger model. We numerically study the effect of disorder in on-site and non-reciprocal hopping terms. Using a real-space winding number, we investigate the impact of disorder on the spectral topology and the anomalous chiral modes under periodic boundary conditions. We discover a remarkable robustness of chiral current under disorder. The value of the chiral current retains the clean system value, is independent of disorder strength and is tracked completely by the real-space winding number for class A which has no symmetries, and class AIII, which has a sub-lattice symmetry. In class $D^{†}$, which has $PT$-symmetric on-site gain and loss terms, we find that the disorder-averaged current is not robust while the winding number is robust. We study the localization physics using the inverse participation ratio and local density of states. As the disorder strength is increased, a mobility-edge phase with a finite winding appears. The abrupt vanishing of the winding number marks a transition from a partially localized to a fully localized phase. Under open boundary conditions, we observe a series of transitions through skin effect-partial skin effect-no skin effect phases. Further, we study the non-Hermitian Anderson skin effect (NHASE) for different symmetry classes, where the system without skin effect develops a disorder-driven skin effect at intermediate disorder values. Remarkably while NHASE is present for different classes, the real-space winding number shows a direct correspondence with it only when all symmetries are broken.

Published version

References in corpus (34)

• Making Sense of Non-Hermitian Hamiltonians
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological Transition in a Non-Hermitian Quantum Walk
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• Observation of higher-order non-Hermitian skin effect
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Many-body localization in a non-Hermitian quasi-periodic system
• Many-body topology of non-Hermitian systems
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• The fate of topological-insulator surface states under strong disorder
• Magnetic suppression of non-Hermitian skin effects
• Non-Hermitian Pseudo-Gaps
• Finite-size effects in non-Hermitian topological systems
• Random matrices beyond the Cartan classification
• Non-Hermitian skin effect as an impurity problem
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Non-Hermitian bidirectional robust transport
• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Modification and Control of Topological Insulator Surface States Using Surface Disorder
• The topological counterparts of non-Hermitian SSH models
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Filling up complex spectral regions through non-Hermitian disordered chains
• Delocalization of non-Hermitian Quantum Walk on Random Media in One Dimension
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models