English

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.

Keywords

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

R2 v1 2026-06-23T01:20:23.844Z