We investigate theoretically the non-linear dynamics of a coupled
nanomechanical oscillator. Under a weak radio frequency excitation, the
resonators can be parametrically tuned into a self-sustained oscillatory
regime. The transfer of electrons from one contact to the other is then
mechanically assisted, generating a rectified current. The direction of the
rectified current is, in most unstable
... [Show full abstract] regions, determined by the phase shift
between the mechanical oscillations and the signal. However, we locate
intriguing parametrical regions of uni-directional rectified current,
suggesting a practical scheme for the realization of a self-powered device in
the nanoscale. In these regions, a dynamical symmetry breaking is induced by
the non-linear coupling of the mechanical and electrical degrees of freedom.
When operating within the Coulomb blockade limit, we locate bands of
instability of enhanced gain.