Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups

TL;DR

This paper classifies and computes the irreducible and co-representations of eighty sets of layer groups, providing a comprehensive resource for understanding their symmetry properties relevant to layered materials.

Contribution

It introduces an efficient symbolic computation method for analyzing layer group symmetries and provides a detailed classification and tabulation of their irreducible representations.

Findings

Classification of irreducible domains based on group actions.

Decomposition of band representations into irreducible components.

Provision of a publicly accessible database of symmetry data.

Abstract

Considered are eighty sets of layer groups, each set consisted of four groups: ordinary single and double, and gray single and double layer group. Structural properties of layer groups (factorization onto cyclic subgroups and existence of grading according to the sequence of halving subgroups) enable efficient symbolic computation (by POLSym code) of the relevant properties, real and complex irreducible and allowed (half-)integer (co-)representations in particular. This task includes, as the first step, classification of the irreducible domains based on the group action in Brillouin zone combined with torus topology. Also, the band (co-)representations induced from the irreducible (co-)representations of Wyckoff position stabilizers (site symmetry groups) are decomposed onto the irreducible components. These, and other layer group symmetry related theoretical data relevant for physics, layered materials in particular, are tabulated and made available through the web site.