  We consider a nanoelectromechanical weak link composed of a carbon nanotube
suspended above a trench in a normal metal electrode and positioned in a gap
between two superconducting leads. The nanotube is treated as a movable
single-level quantum dot in which the position-dependent superconducting order
parameter is induced as a result of Cooper pair tunneling. We show that in such
a system, self-sustained bending vibrations can emerge if a bias voltage is
applied. The occurrence of this effect crucially depends on the direction of
the bias voltage and the relative position of the quantum dot level. We also
demonstrate that the nanotube vibrations strongly affect the dc current through
the system, a characteristic that can be used for the direct experimental
observation of the predicted phenomenon.
