Intrinsic non-Hermitian topological phases

2025/09/08 by Shiozaki, Ken
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2509.06879

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.

Citations

• K-theory classification of Wannier localizability and detachable topological boundary states
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Non-Hermitian physics
• Exceptional topology of non-Hermitian systems
• Topological Origin of Non-Hermitian Skin Effects
• Freed-Moore K-theory
• Classification of topological insulators and superconductors in three spatial dimensions

Related

• Nonsymmorphic Topological Phases of Non-Hermitian Systems
• Unsupervised Classification of Non-Hermitian Topological Phases under Symmetries
• Classifying Order-Two Spatial Symmetries in Non-Hermitian Hamiltonians: Point-gapped AZ and AZ^† Classes
• Topological characterization of phase transitions and critical edge states in one-dimensional non-Hermitian systems with sublattice symmetry
• Exceptional second-order topological insulators