2024/07/23 by Ken Shiozaki, Daichi Nakamura, Shiozaki, Ken +7 · 3 citations
Mathematics · #Algebraic structures and combinatorial models #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2407.18273
openalex publication_date 2024/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions. Remarkably, such Wannier-localizable topological insulators can host boundary states that are detachable from the bulk bands. In our accompanying Letter [D. Nakamura \it et al., Phys. Rev. Lett. 135, 096601 (2025), arXiv:2407.09458], we demonstrate that non-Hermitian topology underlies detachable boundary states in Hermitian topological insulators and superconductors, thereby establishing their tenfold classification based on internal symmetry. Here, using K-theory, we elucidate the relationship between Wannier localizability and detachability of topological boundary states. From the boundary perspective, we classify intrinsic and extrinsic non-Hermitian topology, corresponding to nondetachable and detachable topological boundary states, respectively. From the bulk perspective, on the other hand, we classify Wannier localizability through the homomorphisms of topological phases from the tenfold Altland-Zirnbauer symmetry classes to the threefold Wigner-Dyson symmetry classes. Notably, these two approaches from the boundary and bulk perspectives lead to the same classification. We clarify this agreement and develop a unified understanding of the bulk-boundary correspondence on the basis of K-theory.