Graph theory data for topological quantum chemistry

Vergniory MG, Elcoro L, Wang Z, Cano J, Felser C, Aroyo MI, Andrei Bernevig B, Bradlyn B (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Physical Review E American Physical Society

Book Volume: 96

Article Number: 023310

Journal Issue: 2

DOI: 10.1103/PhysRevE.96.023310

Abstract

Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.

Involved external institutions

Donostia International Physics Center (DIPC) ES Spain (ES) University of Basque Country / Universidad del Pais Vasco (UPV) / Euskal Herriko Unibersitatea (EHU) ES Spain (ES) Princeton University US United States (USA) (US) Max-Planck-Institut für Chemische Physik fester Stoffe (MPI CPfS) / Max Planck Institute for Chemical Physics of Solids DE Germany (DE)

How to cite

APA:

Vergniory, M.G., Elcoro, L., Wang, Z., Cano, J., Felser, C., Aroyo, M.I.,... Bradlyn, B. (2017). Graph theory data for topological quantum chemistry. Physical Review E, 96(2). https://doi.org/10.1103/PhysRevE.96.023310

MLA:

Vergniory, M. G., et al. "Graph theory data for topological quantum chemistry." Physical Review E 96.2 (2017).

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