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(IJCSAM) International Journal of Computing Science and Applied Mathematics(IJCSAM) International Journal of Computing Science and Applied MathematicsGroup theory is a fundamental mathematical framework valuable for analyzing the band structures in materials science. The hexagonal structures have unique electronic structures, 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.
The research successfully implemented a method based on double group theory to analyze the band structures of two-dimensional group-IV and group-V systems.Analysis revealed distinct IR characteristics in both planar and buckled structures, with SOC splitting observed in the Dirac cones.The Z2 invariant calculations confirmed that all group-IV materials are topological insulators, while phosphorene and bismuthene exhibited trivial and topological insulator behavior, respectively.
Penelitian lebih lanjut dapat dilakukan untuk mengeksplorasi pengaruh variasi komposisi dan struktur pada sifat topologi material 2D, misalnya dengan menyelidiki efek doping atau pembentukan heterostruktur. Selain itu, studi komputasi dan eksperimen dapat digabungkan untuk memvalidasi prediksi teoretis dan mengidentifikasi material 2D baru dengan sifat topologi yang diinginkan. Terakhir, penelitian dapat difokuskan pada pengembangan perangkat elektronik baru berdasarkan material 2D topologi, seperti transistor dengan konsumsi daya rendah atau sensor yang sangat sensitif, dengan mempertimbangkan tantangan fabrikasi dan integrasi perangkat.
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