Temperature-dependent layer breathing modes in two-dimensional materials

Relative out-of-plane displacements of the constituent layers of two-dimensional materials give rise to unique low-frequency breathing modes. By computing the height-height correlation functions from molecular dynamics simulations, 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 disulfide $({\mathrm{MoS}}₂)$ are in excellent agreement with available experiments. Our results show a redshift of LBM frequency with an 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. Our Rapid Communication provides a simple and efficient way to probe the interlayer interaction for layered materials and their heterostructures with the inclusion of anharmonic effects.