In-plane Elastic and thermal properties of free-standing Molybdenum Disulfide Membranes measured using Ultrafast Transient Grating Spectroscopy*

Molybdenum disulfide (MoS$_{2}$), a member of transition-metal dichalcogenide (TMDC) family, is of intense interest due to its unique electronic and thermoelectric properties. However, reports of its in-plane thermal conductivity vary due to the difficulty of in-plane thermal conductivity measurements on thin films, and an experimental measurement of the in-plane sound velocity has not been reported. Here, we use transient grating spectroscopy to simultaneously measure the in-plane elastic and thermal properties of free-standing MoS$_{2}$ membranes at room temperature. We obtain a longitudinal acoustic phonon velocity of 7000 $\pm$ 40 m s$^{-1}$ and an in-plane thermal conductivity of 74 $\pm$ 21 Wm$^{-1}$K$^{-1}$. Our measurements provide useful insights into the elastic and thermal properties of MoS$_{2}$ and demonstrate the capability of transient grating spectroscopy to investigate the in-plane vibrational properties of van der Waals materials that are challenging to characterize with conventional methods.