Vibrational instability due to coherent tunneling of electrons

Effects of a coupling between the mechanical vibrations of a quantum dot placed between the two leads of a single-electron transistor and coherent tunneling of electrons through a single level in the dot has been studied. We have found that for bias voltages exceeding a certain critical value a dynamical instability occurs and mechanical vibrations of the dot develop into a stable limit cycle. The current-voltage characteristics for such a transistor were calculated and they seem to be in reasonably good agreement with recent experimental results for the single-C 60 -molecule transistor by Park et al. ( Nature 407 (2000) 57).