Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

Bradlyn B, Elcoro L, Vergniory MG, Cano J, Wang Z, Felser C, Aroyo MI, Bernevig BA (2018)

Publication Type: Journal article

Publication year: 2018

Journal

Physical Review B American Physical Society

Book Volume: 97

Article Number: 035138

Journal Issue: 3

DOI: 10.1103/PhysRevB.97.035138

Abstract

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn, Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local k·p band structures across the Brillouin zone in terms of graph theory. In this paper, we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

Involved external institutions

Princeton University US United States (USA) (US) University of Basque Country / Universidad del Pais Vasco (UPV) / Euskal Herriko Unibersitatea (EHU) ES Spain (ES) Donostia International Physics Center (DIPC) ES Spain (ES) 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:

Bradlyn, B., Elcoro, L., Vergniory, M.G., Cano, J., Wang, Z., Felser, C.,... Bernevig, B.A. (2018). Band connectivity for topological quantum chemistry: Band structures as a graph theory problem. Physical Review B, 97(3). https://doi.org/10.1103/PhysRevB.97.035138

MLA:

Bradlyn, Barry, et al. "Band connectivity for topological quantum chemistry: Band structures as a graph theory problem." Physical Review B 97.3 (2018).

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