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A re-entrant behavior of electron shuttling is shown to occur in a nanoelectromechanical transistor made of magnetic material where spin-polarized electrons are injected into a quantum dot with a single electron level split into two by an external magnetic field. A suppression of shuttle vibrations occurs at a certain value of a bias voltage that starts to allow for transport also through the upper energy level of the dot, while for a further increase of the voltage shuttling recovers. The effect is due to a time-dependent polaronic shift of the dot energy level, which results in a reduction of the supply of electric power to the mechanical motion.

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., 8 pages, 5 figures