Group Theory analysis of phonons in two-dimensional Transition Metal Dichalcogenides

TL;DR

This paper provides a comprehensive group theory analysis of the symmetry properties of transition metal dichalcogenides (TMDCs) as a function of layer number, elucidating their optical and vibrational characteristics.

Contribution

It offers the first detailed group theory framework for understanding symmetry changes in TMDCs with varying layer counts, aiding interpretation of experimental optical data.

Findings

Symmetry changes depend on the number of layers and polytype.

Inversion symmetry plays a crucial role in optical properties.

Optical selection rules and Raman tensors are derived for different layer configurations.

Abstract

Transition metal dichalcogenides (TMDCs) have emerged as a new two dimensional materials field since the monolayer and few-layer limits show different properties when compared to each other and to their respective bulk materials. For example, in some cases when the bulk material is exfoliated down to a monolayer, an indirect-to-direct band gap in the visible range is observed. The number of layers $N$ ($N$ even or odd) drives changes in space group symmetry that are reflected in the optical properties. The understanding of the space group symmetry as a function of the number of layers is therefore important for the correct interpretation of the experimental data. Here we present a thorough group theory study of the symmetry aspects relevant to optical and spectroscopic analysis, for the most common polytypes of TMDCs, i.e. $2Ha$, $2Hc$ and $1T$, as a function of the number of layers. Real space symmetries, the group of the wave vectors, the relevance of inversion symmetry, irreducible representations of the vibrational modes, optical selection rules and Raman tensors are discussed.