Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices
Mathematical Physics
2019-03-11 v3 Mesoscale and Nanoscale Physics
High Energy Physics - Theory
K-Theory and Homology
math.MP
Abstract
A 2-torsion topological phase exists for Hamiltonians symmetric under the wallpaper group with glide reflection symmetry, corresponding to the unorientable cycle of the Klein bottle fundamental domain. We prove a mod 2 twisted Toeplitz index theorem, which implies a bulk-edge correspondence between this bulk phase and the exotic topological zero modes that it acquires along a boundary glide axis.
Cite
@article{arxiv.1804.03945,
title = {Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices},
author = {Kiyonori Gomi and Guo Chuan Thiang},
journal= {arXiv preprint arXiv:1804.03945},
year = {2019}
}
Comments
50 pages, 9 figures. References added, figures improved, Appendix B on integer crystallographic bulk-edge correspondence added, typos corrected for publication in LMP