Projective Representations Construction for Different Points of Brillouin Zone. Application for Space Symmetry Groups $P4_1 2_1 2$ and $P4_3 2_1 2$

TL;DR

This paper introduces a method for constructing irreducible projective representations at various points in the Brillouin zone for specific space groups, considering time inversion effects, to aid in understanding crystal symmetries.

Contribution

It presents a new approach to constructing irreducible projective representations at multiple Brillouin zone points for space groups P4_1 2_1 2 and P4_3 2_1 2, including time inversion effects.

Findings

Constructed one- and two-valued irreducible projective representations at key Brillouin zone points.

Analyzed the influence of time inversion using Herring criterion.

Applied method to specific space groups P4_1 2_1 2 and P4_3 2_1 2.

Abstract

It was suggested method of constructing of irreducible projective representations in different points of Brilluin zone. Points \Gamma, \Lambda, Z, S, A, \Sigma, M, V, R, and X of space symmetry groups $P4_{1}2_{1}2$ and $P4_{3}2_{1}2$ were examined. At each of these points one- and two-valued irreducible projective representations of wave vector groups were constructed for two enantiomorphous modifications. Influence of time inversion at these points also was taken into consideration by means of Herring criterion.