TY - JOUR
T1 - Double crystallographic groups and their representations on the Bilbao Crystallographic Server
AU - Elcoro, Luis
AU - Bradlyn, Barry
AU - Wang, Zhijun
AU - Vergniory, Maia G.
AU - Cano, Jennifer
AU - Felser, Claudia
AU - Andrei Bernevig, B.
AU - Orobengoa, Danel
AU - De La Flor, Gemma
AU - Aroyo, Mois I.
N1 - Funding Information:
Simons Investigator Award, the Packard Foundation and the Schmidt Fund for Innovative Research.
Funding Information:
The work of LE, GF and MIA 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). The work of MGV was supported by FIS2016-75862-P and FIS2013-48286-C2-1-P national projects of the Spanish MINECO. ZW and BAB, 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 and tables, some of the code development, and ab initio work was funded by US Department of Energy de-sc0016239, a
Publisher Copyright:
© 2017 International Union of Crystallography.
PY - 2017/10
Y1 - 2017/10
N2 - 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.
AB - 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.
KW - Bilbao Crystallographic Server
KW - band representations
KW - computer programs
KW - double crystallographic groups
KW - single-valued and double-valued irreducible representations
UR - http://www.scopus.com/inward/record.url?scp=85030647759&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85030647759&partnerID=8YFLogxK
U2 - 10.1107/S1600576717011712
DO - 10.1107/S1600576717011712
M3 - Article
AN - SCOPUS:85030647759
SN - 0021-8898
VL - 50
SP - 1457
EP - 1477
JO - Journal of Applied Crystallography
JF - Journal of Applied Crystallography
IS - 5
ER -