-theory classification of Wannier localizability and detachable topological boundary states
arXiv:2407.18273 · doi:10.1103/hjs9-trrs
Abstract
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 -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 -theory.
arXiv comment12 pages, 1 figure, 4 tables; see also arXiv:2407.09458
References in corpus (39)
- Topological Insulators
- Topological insulators and superconductors
- Classification of topological insulators and superconductors in three spatial dimensions
- Topological Field Theory of Time-Reversal Invariant Insulators
- Classification of topological quantum matter with symmetries
- 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
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Topological Origin of Non-Hermitian Skin Effects
- Topological Band Theory for Non-Hermitian Hamiltonians
- Anomalous edge state in a non-Hermitian lattice
- Non-Bloch Band Theory of Non-Hermitian Systems
- Correspondence between winding numbers and skin modes in non-hermitian systems
- Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
- Wannier representation of Z_2 topological insulators
- Exponential localization of Wannier functions in insulators
- Classification of Exceptional Points and Non-Hermitian Topological Semimetals
- Fragile Topology and Wannier Obstructions
- Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
- Twisted equivariant matter
- Topological surface states in three-dimensional magnetic insulators
- Topological Correspondence between Hermitian and Non-Hermitian Systems: Anomalous Dynamics
- Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
- Refined symmetry indicators for topological superconductors in all space groups
- Exceptional Topological Insulators
- Compactly-supported Wannier functions and algebraic -theory
- On the K-theoretic classification of topological phases of matter
- Non-Hermitian Chiral Skin Effect
- Hermitian Bulk -- Non-Hermitian Boundary Correspondence
- Bulk-boundary correspondence in point-gap topological phases
- Teleportation of Berry curvature on the surface of a Hopf insulator
- Universal platform of point-gap topological phases from topological materials
- Non-Hermitian Topology in Hermitian Topological Matter
- Fragility of surface states in non-Wigner Dyson topological insulators
- Non-Hermitian Origin of Detachable Boundary States in Topological Insulators