@article{17648b68cb2849718bd96f7ea8d8e943,
title = "Graph theory data for topological quantum chemistry",
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.",
author = "Vergniory, {M. G.} and L. Elcoro and Zhijun Wang and Jennifer Cano and C. Felser and Aroyo, {M. I.} and Bernevig, {B. Andrei} and Barry Bradlyn",
note = "Funding Information: B.B. would like to thank Ida Momennejad and Dustin Ngo for fruitful discussions. M.G.V. would like to thank Gonzalo Lopez-Garmendia for help with computational work. B.B., J.C., Z.W., and B.A.B. acknowledge the hospitality of the Donostia International Physics Center, where parts of this work were carried out. J.C. also acknowledges the hospitality of the Kavli Institute for Theoretical Physics, and B.A.B. also acknowledges the hospitality and support of the {\'E}cole Normale Sup{\'e}rieure and Laboratoire de Physique Th{\'e}orique et Hautes Energies. The work of M.V.G. was supported by FIS2016-75862-P and FIS2013-48286-C2-1-P national projects of the Spanish MINECO. The work of L.E. and M.I.A. was supported by the Government of the Basque Country (project IT779-13) and the Spanish Ministry of Economy and Competitiveness and FEDER funds (project MAT2015-66441-P). Z.W. and B.A.B., as well as part of the development of the initial theory and further ab initio work, were supported by the NSF EAGER Grant No. DMR-1643312, ONR-N00014-14-1-0330, ARO MURI W911NF-12-1-0461, and NSF-MRSEC DMR-1420541. The development of the practical part of the theory, tables, some of the code development, and ab initio work was funded by the Department of Energy de-sc0016239, Simons Investigator Award, the Packard Foundation, and the Schmidt Fund for Innovative Research. Publisher Copyright: {\textcopyright} 2017 American Physical Society.",
year = "2017",
month = aug,
day = "28",
doi = "10.1103/PhysRevE.96.023310",
language = "English (US)",
volume = "96",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "2",
}