Skip to main content

Graph theory data for topological quantum chemistry

Author(s): Vergniory, MG; Elcoro, L; Wang, Zhijun; Cano, Jennifer; Felser, C; et al

To refer to this page use:
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)] 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.
Publication Date: 28-Aug-2017
Electronic Publication Date: 28-Aug-2017
Citation: Vergniory, MG, Elcoro, L, Wang, Zhijun, Cano, Jennifer, Felser, C, Aroyo, MI, Andrei Bernevig, B, Bradlyn, Barry. (2017). Graph theory data for topological quantum chemistry. PHYSICAL REVIEW E, 96 (10.1103/PhysRevE.96.023310
DOI: doi:10.1103/PhysRevE.96.023310
ISSN: 2470-0045
EISSN: 2470-0053
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW E
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.