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Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices

  • Kiyonori Gomi
  • Guo Chuan Thiang
Article
  • 52 Downloads

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

Bulk-edge correspondence Topological crystalline insulators Twisted K-theory Toeplitz index theorem 

Mathematics Subject Classification

19L50 19K56 47L80 

Notes

Acknowledgements

G.C.T. is supported by ARC grant DE170100149 and would like to thank G. De Nittis, V. Mathai and K. Hannabuss for helpful discussions. He also acknowledges H.-H. Lee for his kind hospitality at the Seoul National University, where part of this work was completed. K.G. is supported by JSPS KAKENHI Grant Number JP15K04871, and thanks I. Sasaki, M. Furuta and K. Shiozaki for useful discussions.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesShinshu UniversityMatsumotoJapan
  2. 2.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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