Zusammenfassung
A new section of databases and programs devoted to double crystallographic
groups (point and space groups) has been implemented in the Bilbao
Crystallographic Server (<a href="http://www.cryst.ehu.es">this http URL</a>). 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 DCOMPATIBILITY
RELATIONS 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 and the search of topological insulators.
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