Shear and breathing modes of layered materials

TL;DR

This paper introduces a general, symmetry-based method to predict and interpret the Raman and infrared spectroscopic modes of layered materials with any number of identical layers, aiding material characterization.

Contribution

It combines a mechanical model with group theory to accurately predict spectroscopic fan diagrams for multilayer materials, implemented in an open-source tool.

Findings

Predicts complete fan diagrams for shear and breathing modes

Identifies Raman and infrared active modes across layer numbers

Provides an open-source tool for researchers

Abstract

Layered materials (LMs), such as graphite, hexagonal boron nitride, and transition-metal dichalcogenides, are at the centre of an ever increasing research effort, due to their scientific and technological relevance. Raman and infrared spectroscopies are accurate, non-destructive, approaches to determine a wide range of properties, including the number of layers and the strength of the interlayer interactions. Here, we present a general approach to predict the complete spectroscopic fan diagrams, i.e., the relations between frequencies and number of layers, $N$, for the optically-active shear and layer-breathing modes of any multilayer comprising $N \geq 2$ identical layers. In order to achieve this, we combine a description of the normal modes in terms of a one-dimensional mechanical model, with symmetry arguments that describe the evolution of the point group as a function of $N$. Group theory is then used to identify which modes are Raman and/or infrared active, and to provide diagrams of the optically-active modes for any stack composed of identical layers. We implement the method and algorithms in an open-source tool directly available on the Materials Cloud portal, to assist any researcher in the prediction and interpretation of such diagrams. Our work will underpin all future efforts on Raman and Infrared characterization of known, and yet not investigated, LMs.