Non-Hermitian Origin of Detachable Boundary States in Topological Insulators

Abstract

While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non-Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. Based on this connection and $K$-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states.

7+8 pages, 4+5 figures, 2+1 tables; see also arXiv:2407.18273

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Cited by in corpus (8)

• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Topology of ultra-localized insulators and superconductors
• Frustration-free free fermions and beyond
• Intrinsic non-Hermitian topological phases
• Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors
• Breakdown of the symmetry constraint in a Floquet topological insulator
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field