Graphene resonator as an ultrasound detector for generalized Love waves in a polymer film with two level states

We have investigated surface shear waves at 22 MHz in a 0.5-micron-thick polymer film on SiO2/Si substrate at low temperatures using suspended and non-suspended graphene as detectors. By tracking ultrasound modes detected by oscillations of a trilayer graphene membrane both in vacuum and in helium superfluid, we assign the resonances to surface shear modes, generalized Love waves, in the resist/silicon-substrate system loaded with gold. The propagation velocity of these shear modes displays a logarithmic temperature dependence below 1 K, which is characteristic for modification of the elastic properties of a disordered solid owing to a large density of two level state (TLS) systems. For the dissipation of the shear mode, we find a striking logarithmic temperature dependence, which indicates a basic relation between the speed of the surface wave propagation and the mode dissipation.