Dimensional crossover of acoustic phonon lifetime in $2H$-MoSe$_2$

A time-resolved observation of coherent interlayer longitudinal acoustic phonons in 2$H$-MoSe$_2$ is reported. A femtosecond pump-probe technique is used to investigate the evolution of the energy loss of these vibrational modes in a wide selection of MoSe$_2$ flakes with different thicknesses ranging from bilayer up to the bulk limit. By directly analysing the temporal decay of the modes, we can clearly distinguish an abrupt crossover related to the acoustic mean free path of the phonons in a layered system, and the constraints imposed to the acoustic decay channels when reducing the dimensionality. Loses intrinsic to the low dimensionality of single or few layer materials impose critical limitations for their use in optomechanical and optoelectronic devices.