Surface State Electronic Characteristics and \(\mathbb {Z}_2\) Topological Invariant of \(Bi_2Te_3\) Topological Insulator Through PBE and LmBJ Potential

A topological insulator (TI) is characterized by its band inversion (in its bulk) which is caused by the strong spin-orbit interaction and an exotic metallic state in its surface. In this work, using a DFT study, we prove that \(Bi_2Te_3\) has a band inversion in its bulk form and becomes conducting in its surface. The existence of single band inversion is analyzed with PBE and TB-mBJ potential taking spin-orbit interaction into consideration. The metallic surface state is confirmed with the PBE and LmBJ potential. The LmBJ potential enables the study of heterogeneous, finite, and low-dimensional systems and has not been studied yet for \(Bi_2Te_3\). We also prove that \(Bi_2Te_3\) is a \( \mathbb {Z}_2 \) topological insulator from the \( \mathbb {Z}_2 \) invariant calculation by computing an evolution of hybrid Wannier charge centers.