Theoretical study on $d$-orbital structures in low dimensional materials

Abstract

In this dissertation, we theoretically analyzed $d$-orbital structures in 2-dimensional transition metal dichalcogenides(TMD). We discover that the orbital structures are determined by the symmetries of the atomic structure. On trigonal prismatic H-TMDs, $C_3$ rotational symmetry induces $sp^2$-like hybrid $d$-orbitals. Due to orbital ordering in the material, these hybrid orbitals form a breathing Kagome lattice. It becomes a topological insulator, an obstructed atomic limit insulator, due to strong inter-site hybridization. These inter-site bonding give 0-dimensional electronic structures, that are analogous to that of molecular orbitals in benzene, and becomes a pathological example for a DFT$+U$ method, which corrects the local correlation effect. On octahedral T-TMDs, $t_{2g}$ orbitals from the crystal field form 1D chains. This chain model can reveal the T to T$'$ transition mechanism for MoS$_2$. We expect that these findings could provide a new methodology to understand fundamental $d$-orbital structures in 2 dimensional beyond TMDs.