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  Building blocks of topological quantum chemistry: Elementary band representations

Cano, J., Bradlyn, B., Wang, Z., Elcoro, L., Vergniory, M. G., Felser, C., et al. (2018). Building blocks of topological quantum chemistry: Elementary band representations. Physical Review B, 97(3): 035139, pp. 1-20. doi:10.1103/PhysRevB.97.035139.

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Datensatz-Permalink: http://hdl.handle.net/21.11116/0000-0000-643D-C Versions-Permalink: http://hdl.handle.net/21.11116/0000-0000-6441-6
Genre: Zeitschriftenartikel

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 Urheber:
Cano, Jennifer1, Autor
Bradlyn, Barry1, Autor
Wang, Zhijun1, Autor
Elcoro, L.1, Autor
Vergniory, M. G.1, Autor
Felser, C.2, Autor              
Aroyo, M. I.1, Autor
Bernevig, B. Andrei1, Autor
Affiliations:
1External Organizations, escidoc:persistent22              
2Claudia Felser, Inorganic Chemistry, Max Planck Institute for Chemical Physics of Solids, Max Planck Society, escidoc:1863429              

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Schlagwörter: -
 Zusammenfassung: The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time reversal in his theory of "elementary" band representations. In a recent paper [Bradlyn et al., Nature (London) 547, 298 (2017)] we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localizedWannier orbitals respecting the symmetries of the lattice (including time reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wave functions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

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Sprache(n): eng - Englisch
 Datum: 2018-01-162018-01-16
 Publikationsstatus: Im Druck publiziert
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: -
 Identifikatoren: DOI: 10.1103/PhysRevB.97.035139
 Art des Abschluß: -

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Titel: Physical Review B
  Kurztitel : Phys. Rev. B
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: Woodbury, NY : American Physical Society
Seiten: - Band / Heft: 97 (3) Artikelnummer: 035139 Start- / Endseite: 1 - 20 Identifikator: ISSN: 1098-0121
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925225008