Quantum theory of magnetoelectromotive instability in nanoelectromechanical systems with positive differential conductance.

We consider dc-electronic transport through a nanowire suspended between two normal-metal leads in the presence of an external magnetic field. We show the very mechanism through which such a system, whose stationary current-voltage characteristic is essentially characterized by positive differential conductance, becomes unstable with respect to an onset of self-excited oscillations in electrical transport and mechanical vibrations. The self-excitation mechanism is based on the correlation between the occupancy of the quantized spin-split electronic energy levels inside the nanowire and the velocity of the nanowire with the crucial influence of strong enough retardation effects in magnetomotive coupling coming from mechanical vibrations.