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

Abstract

Considered are 80 sets of layer groups, each set consisting of four groups: ordinary single and double, and grey single and double layer groups. The structural properties of layer groups (factorization into cyclic subgroups and the existence of grading according to the sequence of halving subgroups) enable efficient symbolic computation (by the 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 the 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 into 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 https://nanolab.group/layer/.