Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -

Author
Shiozaki, Ken · Sato, Masatoshi · Gomi, Kiyonori
Year 2017
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Abstract

We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an application of our formulation, we present a complete classification of topological crystalline surface states, in the absence of time-reversal invariance. The classification works for gapless surface states of three-dimensional insulators, as well as full gapped two-dimensional insulators. Such surface states and two-dimensional insulators are classified in a unified way by 17 wallpaper groups, together with the presence or the absence of (sublattice) chiral symmetry. We identify the topological numbers and their representations under the wallpaper group operation. We also exemplify the usefulness of our formulation in the classification of bulk gapless phases. We present a new class of Weyl semimetals and Weyl superconductors that are topologically protected by inversion symmetry.

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Details

Title
Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
Author
Shiozaki, Ken · Sato, Masatoshi · Gomi, Kiyonori
Year
2017
Journal*
Phys. Rev. B 95, 235425 (2017)
Type
Research Article
Language
eng
Comment
72 pages
History
2017-01-30 00:00:00 · 2017-02-19 00:00:00 · 2017-03-21 00:00:00 · 2017-06-09 00:00:00
Categories
Mathematical Physics · Mesoscopic Systems and Quantum Hall Effect · Superconductivity · Condensed Matter

Fields edited by Q-Sensei or Q-Sensei's users are marked with an asterisk (*).
This is Version 4 of this record. Q-Sensei Corp. added this version on June 30, 2017. It is an edited version of the original data import from arXiv.org e-Print archive. View changes to the previous version or view the complete version history.