  We propose and analyze the detector of modulated terahertz (THz) radiation
based on the graphene field-effect transistor with mechanically floating gate
made of graphene as well. The THz component of incoming radiation induces
resonant excitation of plasma oscillations in graphene layers (GLs). The
rectified component of the ponderomotive force between GLs invokes resonant
mechanical swinging of top GL, resulting in the drain current oscillations. To
estimate the device responsivity, we solve the hydrodynamic equations for the
electrons and holes in graphene governing the plasma-wave response, and the
equation describing the graphene membrane oscillations. The combined
plasma-mechanical resonance raises the current amplitude by up to four orders
of magnitude. The use of graphene as a material for the elastic gate and
conductive channel allows the voltage tuning of both resonant frequencies in a
wide range.
