Shear and breathing modes of layered materials

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 $N\ge 2$ 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.

30 pages (including appendices and tables), 7 figures

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• Raman Forbidden Layer-Breathing Modes in Layered Semiconductor Materials Activated by Phonon and Optical Cavity Effects
• Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups
• Dominant two-dimensional electron-phonon interactions in the bulk Dirac semimetal Na3Bi
• Giant Shear Displacement by Light-Induced Raman Force in Bilayer Graphene
• Light-induced shear phonon splitting and instability in bilayer graphene