Applications of Double Group Theory in 2D Materials

Muhammad Yusuf Hakim Widianto (Departemen Matematika, Institut Teknologi Sepuluh Nopember)
Mineo Saito (Faculty of Mathematics and Physics, Institute of Science and Technology, Kanazawa University, Kanazawa)

International Journal of Computing Science and Applied Mathematics
Vol 9, No 2 (2023)

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 Z2 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.