Topology of Wannierizable Insulators
Abstract
We study the freedom in choosing Wannier centers and the associated symmetry representations in noninteracting Wannierizable insulators. We compare Wyckoff deformations of atomic configurations with symmetry-preserving adiabatic deformations of occupied states, both with and without adding common occupied atomic orbitals. Explicit examples show that stable Wyckoff equivalence and adiabatic equivalence at fixed filling do not imply each other. In spinless Fm'm'm', an Euler class distinguishes stably Wyckoff-equivalent configurations. In spinless P1̅', adiabatically equivalent configurations remain distinct under stable Wyckoff deformations. We also classify when stable Wyckoff and stable adiabatic equivalence coincide. They agree in two or fewer dimensions and in three-dimensional spinful systems. For three-dimensional spinless systems, Chern insulator pumps give additional equivalences in 134 magnetic space groups. These groups preserve spacetime orientation and have a point whose site-symmetry group contains $222$, 1̅', or 4̅'.
Related
- Band mixing and particle-hole asymmetry in moire fractional Chern insulators
- Spinless and Spinful Charge Excitations in Moiré Fractional Chern Insulators
- Divergent Orbital Diamagnetism from Chiral Edge States in Chern Insulators
- Nonlinearity-Induced Suppression of Dissipation in Bath-Coupled Floquet Topological Insulators
- Quantum-Geometric Subgap Second-Harmonic Generation in PT-Symmetric Antiferromagnetic Insulators
BibTeX
@misc{shiozaki2026topology,
title = {{Topology of Wannierizable Insulators}},
author = {Ken Shiozaki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38626},
eprint = {2610.38626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38626},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topology of Wannierizable Insulators
AU - Ken Shiozaki
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38626
UR - https://arxiv.org/abs/2610.38626
AB - We study the freedom in choosing Wannier centers and the associated symmetry representations in noninteracting Wannierizable insulators. We compare Wyckoff deformations of atomic configurations with symmetry-preserving adiabatic deformations of occupied states, both with and without adding common occupied atomic orbitals. Explicit examples show that stable Wyckoff equivalence and adiabatic equivalence at fixed filling do not imply each other. In spinless Fm'm'm', an Euler class distinguishes stably Wyckoff-equivalent configurations. In spinless P1̅', adiabatically equivalent configurations remain distinct under stable Wyckoff deformations. We also classify when stable Wyckoff and stable adiabatic equivalence coincide. They agree in two or fewer dimensions and in three-dimensional spinful systems. For three-dimensional spinless systems, Chern insulator pumps give additional equivalences in 134 magnetic space groups. These groups preserve spacetime orientation and have a point whose site-symmetry group contains $222$, 1̅', or 4̅'.
ER -