Crystal field, ligand field, and interorbital effects in two-dimensional transition metal dichalcogenides across the periodic table

TL;DR

This paper quantifies crystal and ligand field effects in two-dimensional transition metal dichalcogenides using Wannier functions, revealing the dominant role of orbital hybridization and trends across the periodic table.

Contribution

It applies a Wannier-function approach to separate and analyze crystal and ligand field contributions in 2D TMDs, providing new insights into their stability and electronic properties.

Findings

Ligand field slightly stabilizes the 1H polymorph in some TMDs.

Hybridization between d orbitals is the main factor influencing properties.

Trends across the periodic table are explained by charge-transfer energy variations.

Abstract

Two-dimensional transition metal dichalcogenides (TMDs) exist in two polymorphs, referred to as $1T$ and $1H$, depending on the coordination sphere of the transition metal atom. The broken octahedral and trigonal prismatic symmetries lead to different crystal and ligand field splittings of the $d$ electron states, resulting in distinct electronic properties. In this work, we quantify the crystal and ligand field parameters of two-dimensional TMDs using a Wannier-function approach. We adopt the methodology proposed by Scaramucci et al. [A. Scaramucci et al., J. Phys.: Condens. Matter 27, 175503 (2015)]. that allows to separate various contributions to the ligand field by choosing different manifolds in the construction of the Wannier functions. We discuss the relevance of the crystal and ligand fields in determining the relative stability of the two polymorphs as a function of the filling of the $d$-shell. Based on the calculated parameters, we conclude that the ligand field, while leading to a small stabilizing factor for the $1H$ polymorph in the $d^1$ and $d^2$ TMDs, plays mostly an indirect role and that hybridization between different $d$ orbitals is the dominant feature. We investigate trends across the periodic table and interpret the variations of the calculated crystal and ligand fields in terms of the change of charge-transfer energy, which allows developing simple chemical intuition.