Time-domain response of atomically thin $\mathrm{M}\mathrm{o}{\mathrm{S}}_2$ nanomechanical resonators

We measure the energy relaxation rate of single- and few-layer molybdenum disulphide ($\mathrm{M}\mathrm{o}{\mathrm{S}}_2$) nanomechanical resonators by detecting the resonator ring-down. Recent experiments on these devices show a remarkably low quality (Q)-factor when taking spectrum measurements at room temperature. The origin of the low spectral Q-factor is an open question, and it has been proposed that besides dissipative processes, frequency fluctuations contribute significantly to the resonance line-width. The spectral measurements performed thus far however, do not allow one to distinguish these two processes. Here, we use time-domain measurements to quantify the dissipation. We compare the Q-factor obtained from the ring-down measurements to those obtained from the thermal noise spectrum and from the frequency response of the driven device. In few-layer and single-layer $\mathrm{M}\mathrm{o}{\mathrm{S}}_2$ resonators the two are in close agreement, which demonstrates that the spectral line-width in $\mathrm{M}\mathrm{o}{\mathrm{S}}_2$ membranes at room temperature is limited by dissipation, and that excess spectral broadening plays a negligible role.