Applications of Double Group Theory in 2D Materials

Abstract

Group theory is a fundamental mathematical frame- work valuable for analyzing the band structures in materials science. The hexagonal structures have unique electronic struc- tures, especially in 2D materials in group-IV, where the system is observed as the topological insulator. Meanwhile, in the case of group-V, it is semiconductors. This paper analyzes group- IV and group-V band structures based on group theory and proposes a method to identify the irreducible representation (IR) in symmorphic systems. It is found that all materials in group- IV are topological insulators. The evaluation of Z 2 invariant v in group-V found that the phosphorene and bismuthene cases are v = 0 and v = 1 , respectively, and belong to trivial and topological insulator materials for phosphorene and bismuthene, respectively.