Graph theory data for topological quantum chemistry

M. G. Vergniory, L. Elcoro, Zhijun Wang, Jennifer Cano, C. Felser, M. I. Aroyo, B. Andrei Bernevig, Barry Bradlyn

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


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.

Original languageEnglish (US)
Article number023310
JournalPhysical Review E
Issue number2
StatePublished - Aug 28 2017

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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