Probing the acoustic losses of graphene with a low-loss quartz bulk-acoustic-wave resonator at cryogenic temperatures
We observe mechanical effects of an exfoliated graphene monolayer deposited on a quartz crystal substrate designed to operate as an extremely low-loss bulk-acoustic-wave cavity at liquid-helium temperature.This is achieved by sensing overtones of the three thickness eigen-modes of the so-called SC-cut, since all three modes, two shear mode and one extensional mode, can be electrically probed with such a crystal cut. From quality-factor measurements, the mechanical losses of the adhesive graphene monolayer are assessed to be about 8 x 10-4 at 4 K in the best case. They are therefore significantly greater than those already reported for suspended membranes but also for adherent layers on SiO2/Si substrates operating in torsional modes. In fact, results reveal that surface scattering occurs due to a roughness degradation of a factor 7. In addition, the mechanical losses presented here are also placed in the context of a device submitted to thermomechanical stresses, but which are not the only ones existing. Some of them could be intrinsic ones related to the deposition process of the graphene layer. Based on a force-frequency theory applied to the three thickness modes which react differently to stresses, it is demonstrated that this stress effect actually entangled with that of mass loading reconciles the experimental results.