Layer groups: Brillouin-zone and crystallographic databases on the Bilbao Crystallographic Server.

Area of Science:

• Crystallography
• Solid-state Physics
• Materials Science

Background:

• The Bilbao Crystallographic Server provides specialized databases for subperiodic groups.
• Layer groups are fundamental in understanding crystal structures and their properties.
• Existing classifications of irreducible representations for layer groups can present challenges in uniqueness and completeness.

Purpose of the Study:

• To present comprehensive crystallographic and Brillouin-zone databases for all 80 layer groups.
• To provide tools for the classification of irreducible representations of layer groups.
• To address issues of uniqueness and completeness in layer-group representations.

Main Methods:

• Utilizing the Bilbao Crystallographic Server's dedicated section for subperiodic groups.
• Compiling crystallographic databases: generators/general positions (GENPOS), Wyckoff positions (WYCKPOS), and maximal subgroups (MAXSUB).
• Developing the Brillouin-zone database (LKVEC) with k-vector tables and figures, employing the reciprocal-space-group approach.

Main Results:

• The crystallographic databases (GENPOS, WYCKPOS, MAXSUB) are now available for layer groups.
• The LKVEC database provides k-vector tables and Brillouin-zone figures for all 80 layer groups.
• A detailed specification of independent parameter ranges for k vectors is provided, enhancing representation analysis.

Conclusions:

• The presented databases and methods offer a robust framework for studying layer groups and their representations.
• The work facilitates a deeper understanding of symmetry properties in crystalline materials.
• This resource aids researchers in solving problems related to the uniqueness and completeness of layer-group representations.