  We predict and analyze mechanical instability and corresponding
self-sustained mechanical oscillations occurring in a nanoelectromechanical
system composed of a metallic carbon nanotube (CNT) suspended between two
superconducting leads and coupled to a scanning tunneling microscope (STM) tip.
We show that such phenomena are realized in the presence of both the coherent
Andreev tunneling between the CNT and superconducting leads, and an incoherent
single electron tunneling between the voltage biased STM tip and CNT. Treating
the CNT as a single-level quantum dot, we demonstrate that the mechanical
instability is controlled by the Josephson phase difference, relative position
of the electron energy level, and the direction of the charge flow. It is found
numerically that the emergence of the self-sustained oscillations leads to a
substantial suppression of DC electric current.
