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.

arXiv commentPublished version

References in corpus (90)

• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Topological Transition in a Non-Hermitian Quantum Walk
• Non-Hermitian Topological Invariants in Real Space
• Critical non-Hermitian Skin Effect
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Higher-order non-Hermitian skin effect
• New topological invariants in non-Hermitian systems
• Experimental realization of a Weyl exceptional ring
• Observation of higher-order non-Hermitian skin effect
• Observation of arbitrary topological windings of a non-Hermitian band
• Non-Hermitian Many-Body Localization
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Topological states of non-Hermitian systems
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Tenfold Way for Quadratic Lindbladians
• Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system
• Disordered Topological Insulators: A Non-Commutative Geometry Perspective
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Skin effect and winding number in disordered non-Hermitian systems
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Impurity induced scale-free localization
• Non-Hermitian Topological Anderson Insulators
• Nonunitary Scaling Theory of Non-Hermitian Localization
• 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
• Entanglement spectrum and symmetries in non-Hermitian fermionic non-interacting models
• Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equation
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Exceptional Points in a Non-Hermitian Topological Pump
• Exceptional Topological Insulators
• Topological Field Theory of Non-Hermitian Systems
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• The fate of topological-insulator surface states under strong disorder
• Experimental realization of sensitivity enhancement and suppression with exceptional surfaces
• Magnetic suppression of non-Hermitian skin effects
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• 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
• Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems
• Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models
• Non-Hermitian bidirectional robust transport
• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Non-Hermitian anomalous skin effect
• Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model
• The topological counterparts of non-Hermitian SSH models
• Modification and Control of Topological Insulator Surface States Using Surface Disorder
• Disorder driven phase transitions in weak AIII topological insulators
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• 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