Trigonal Symmetry Breaking and its Electronic Effects in Two-Dimensional Dihalides and Trihalides

TL;DR

This paper investigates how trigonal symmetry influences the electronic structure of 2D halide materials, revealing how symmetry breaking can lead to diverse electronic states and offering a framework for tuning these states.

Contribution

It provides a comprehensive analysis of trigonal symmetry effects on electronic states in 2D halides using Wannier models and examples like ZrI2 and CuCl2, highlighting new pathways for electronic state control.

Findings

Trigonal symmetry causes specific orbital splitting in 2D halides.

Symmetry breaking can induce orbitally polarized magnetic and Mott states.

A framework for understanding and tuning electronic states in low-dimensional halides.

Abstract

We study the consequences of the approximately trigonal ($D_{3d}$) point symmetry of the transition metal (M) site in two-dimensional van der Waals MX$_2$ dihalides and MX$_3$ trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal $d$ shell, which may be tuned by the interlayer distance, and changes in the ligand-ligand bond lengths. Orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ZrI$_2$ and CuCl$_2$ as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analysing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and $p$-$d$ orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states. Our work establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Our analysis shows that trigonal symmetry and its breaking is a key feature of the 2D halides that needs to be accounted for in search of novel electronic states in materials ranging from CrI$_3$ to $\alpha$-RuCl$_3$.