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

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.

50 pages, 9 figures. References added, figures improved, Appendix B on integer crystallographic bulk-edge correspondence added, typos corrected for publication in LMP

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Cited by in corpus (7)

• Topological characterization of classical waves: the topological origin of magnetostatic surface spin waves
• Index theory and topological phases of aperiodic lattices
• Good Wannier bases in Hilbert modules associated to topological insulators
• Classifying bulk-edge anomalies in the Dirac Hamiltonian
• Topological Spectral Bands with Frieze Groups
• Local symmetry groups for arbitrary wavevectors
• Lieb-Schultz-Mattis Theorem and the Filling Constraint