5 research outputs found
Double crystallographic groups and their representations on the Bilbao Crystallographic Server
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 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.Comment: 32 pages, 20 figures. Two extra figures and minor typo mistakes
fixed. Published versio
Brillouin-zone database on the Bilbao Crystallographic Server
The Brillouin-zone database of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) offers k-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknell et al. [Kronecker Product Tables, Vol. 1, General Introduction and Tables of Irreducible Representations of Space Groups (1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and special k vectors. Guides to the k-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples
The Site-Symmetry Induced Representations Of Layer Groups On The Bilbao Crystallographic Server
The program LSITESYM of the Bilbao Crystallographic Server (http://www.cryst.ehu.es), which establishes symmetry relations between localized and extended states in crystals with layer symmetry, is presented. The utility of the program is discussed and illustrated with several examples., The section of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) dedicated to subperiodic groups includes a new tool called LSITESYM for the study of materials with layer and multilayer symmetry. This new program, based on the site-symmetry approach, establishes the symmetry relations between localized and extended crystal states using representations of layer groups. The efficiency and utility of the program LSITESYM is demonstrated by illustrative examples, which include the analysis of phonon symmetry in Aurivillius compounds and in van der Waals layered crystals MoS2 and WS2.PubMedWoSScopu