Parametric excitation of a dc shuttle current via spontaneous symmetry   breaking
  We investigate theoretically the dynamics of a spatially symmetric shuttle-system subjected to an ac gate voltage. We demonstrate that in such a system parametric excitation gives rise to mechanical vibrations when the frequency of the ac signal is close to the eigenfrequency of the mechanical subsystem. These mechanical oscillations result in a dc shuttle current in a certain direction due to spontaneous symmetry breaking. The direction of the current is defined by the phase shift between the ac gate voltage and the parametrically excited mechanical oscillations. Dependance of the shuttle current on the dc gate voltage is also analyzed. 
Milton E. Pena-Aza, Alessandro Scorrano, and Leonid Y. Gorelik
cond-mat.mes-hall