Intrinsic non-Hermitian topological phases

Abstract

We study the interplay of non-Hermitian topological phases under point- and line-gap conditions. Using natural homomorphisms from line-gap to point-gap phases, we distinguish extrinsic phases, reducible to Hermitian or anti-Hermitian line-gapped phases, from intrinsic phases, which are genuinely non-Hermitian without Hermitian counterparts. Although classification tables for all symmetry classes were already presented in earlier work, the present paper develops a unified formulation and provides explicit computations for all internal symmetries.

33 pages

References in corpus (30)

• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• 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
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topology of crystalline insulators and superconductors
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian topological phenomena: A review
• Topological Non-Hermitian skin effect
• Twisted equivariant matter
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Exceptional Topological Insulators
• Topological Field Theory of Non-Hermitian Systems
• On the K-theoretic classification of topological phases of matter
• A Classification of Non-Hermitian Random Matrices
• Bulk-boundary correspondence in point-gap topological phases
• Symmetry indicator in non-Hermitian systems
• Fragility of surface states in non-Wigner Dyson topological insulators
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• $K$-theory classification of Wannier localizability and detachable topological boundary states