  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.
