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Annual Review of Condensed Matter Physics

Volume 12, 2021

Band Representations and Topological Quantum Chemistry

Abstract

In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space. Next, we introduce the concept of a band representation, which quantifies the symmetry of topologically trivial band structures. By combining band representations with symmetry constraints on the connectivity of bands in momentum space, we show how topologically nontrivial bands can be cataloged and classified. We present several examples of new topological phases discovered using this paradigm and conclude with an outlook toward future developments.

Keyword(s): band theory of solids, crystal symmetry, topological insulators
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/content/journals/10.1146/annurev-conmatphys-041720-124134
2021-03-10
2025-04-19
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Band Representations and Topological Quantum Chemistry
Annual Review of Condensed Matter Physics 12, 225 (2021); https://doi.org/10.1146/annurev-conmatphys-041720-124134
/content/journals/10.1146/annurev-conmatphys-041720-124134
/content/journals/10.1146/annurev-conmatphys-041720-124134
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