Non-Hermitian Topology in Hermitian Topological Matter

Abstract

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our work uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.

9+10 pages, 5+1 figures

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Cited by in corpus (10)

• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Exceptional second-order topological insulators
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Non-Hermitian Hopf insulators
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Phase transition from Weyl to self-linked semimetal using bi-circular laser
• Emergence of Hermitian topology from non-Hermitian knots