Double crystallographic groups and their representations on the Bilbao Crystallographic Server

Luis Elcoro, Barry Bradlyn, Zhijun Wang, Maia G. Vergniory, Jennifer Cano, Claudia Felser, B. Andrei Bernevig, Danel Orobengoa, Gemma De La Flor, Mois I. Aroyo

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48 Scopus citations

Abstract

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single-and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPG and REPRESENTATIONS DSG). The tool DCOMPREL provides compatibility relations between the irreducible representations of double space groups at different k vectors of the Brillouin zone when there is a group-subgroup relation between the corresponding little groups. The program DSITESYM implements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the program BANDREP calculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results of BANDREP have been extensively applied in the description of and the search for topological insulators.A new section of computer tools devoted to the double crystallographic groups has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The section includes databases of symmetry operations and irreducible representations of the double point and space groups and programs that compute the compatibility relations, generate relevant information related to the site-symmetry approach, and calculate band representations and elementary band representations induced from any Wyckoff position of any double space group.

Original languageEnglish (US)
Pages (from-to)1457-1477
Number of pages21
JournalJournal of Applied Crystallography
Volume50
Issue number5
DOIs
StatePublished - Oct 2017

All Science Journal Classification (ASJC) codes

  • Biochemistry, Genetics and Molecular Biology(all)

Keywords

  • Bilbao Crystallographic Server
  • band representations
  • computer programs
  • double crystallographic groups
  • single-valued and double-valued irreducible representations

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    Elcoro, L., Bradlyn, B., Wang, Z., Vergniory, M. G., Cano, J., Felser, C., Andrei Bernevig, B., Orobengoa, D., De La Flor, G., & Aroyo, M. I. (2017). Double crystallographic groups and their representations on the Bilbao Crystallographic Server. Journal of Applied Crystallography, 50(5), 1457-1477. https://doi.org/10.1107/S1600576717011712