Temperature Dependent Layer Breathing Modes in Two Dimensional Materials

TL;DR

This paper investigates layer breathing modes in two-dimensional materials, showing how their frequencies depend on thickness and temperature, and providing a simple model to understand interlayer interactions including anharmonic effects.

Contribution

It introduces a linear chain model to map layer breathing modes and predicts their behavior in various 2D materials considering anharmonicities.

Findings

LBM frequencies decrease with increasing temperature.

Model predictions match experimental data for graphene and MoS2.

Thickness influences LBM frequency shifts.

Abstract

Relative out of plane displacements of the constituent layers of two dimensional materials gives rise to unique low frequency breathing modes. By computing the height-height correlation functions in momentum space, we show that, the layer breathing modes (LBMs) can be mapped consistently to vibrations of a simple linear chain model. Our calculated thickness dependence of LBM frequencies for few layer (FL) graphene and molybdenum disulphide (MoS$_{2}$) are in excellent agreement with available experiments. Our results show a redshift of LBM frequency with increase in temperature, which is a direct consequence of anharmonicities present in the interlayer interaction. We also predict the thickness and temperature dependence of LBM frequencies for FL hexagonal boron nitride (hBN). Our study provides a simple and efficient way to probe the interlayer interaction for layered materials and their heterostructures, with the inclusion of anharmonic effects.