Real-space topological localizer index to fully characterize the dislocation skin effect

Abstract

The dislocation skin effect exhibits the capacity of topological defects to trap an extensive number of modes in two-dimensional non-Hermitian systems. Similar to the corresponding skin effects caused by system boundaries, this phenomenon also originates from nontrivial topology. However, finding the relationship between the dislocation skin effect and nonzero topological invariants, especially in disordered systems, can be obscure and challenging. Here, we introduce a real-space topological invariant based on the spectral localizer to characterize the skin effect on two-dimensional lattices. We demonstrate that this invariant consistently predicts the occurrence and location of both boundary and dislocation skin effects, offering a unified approach applicable to both ordered and disordered systems. Our work demonstrates a general approach that can be utilized to diagnose the topological nature of various types of skin effects, particularly in the absence of translational symmetry when momentum-space descriptions are inapplicable.

arXiv comment8 pages, 6 figures

References in corpus (36)

• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Periodic table for topological insulators and superconductors
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Kwant: a software package for quantum transport
• Non-Hermitian Boundary Modes
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Biorthogonal Quantum Mechanics
• Non-Hermitian topological phenomena: A review
• Acoustic non-Hermitian skin effect from twisted winding topology
• Topological Non-Hermitian skin effect
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• K-Theory and Pseudospectra for Topological Insulators
• Aperiodic Weak Topological Superconductors
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Dislocation Non-Hermitian Skin Effect
• Local invariants identify topology in metals and gapless systems
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian skin effect of dislocations and its topological origin
• Index pairings in presence of symmetries with applications to topological insulators
• Non-Hermitian dislocation modes: Stability and melting across exceptional points
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory
• Invariants of disordered semimetals via the spectral localizer
• Bulk Spectrum and K-theory for Infinite-Area Topological Quasicrystal
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Spectral localizer for line-gapped non-hermitian systems
• Chern numbers as half-signature of the spectral localizer
• Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants

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• Laser-induced topological phases in monolayer amorphous carbon
• Dimensional crossover of class D real-space topological invariants
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases