Magnetomotive Instability and Generation of Mechanical Vibrations in Suspended Semiconducting Carbon Nanotubes

We have theoretically investigated the electromechanical properties of a freely suspended carbon nanotube that is connected to a constant-current source and subjected to an external magnetic field. We show that self-excitation of mechanical vibrations of the nanotube can occur if the magnetic field $H$ exceeds a dissipation-dependent critical value $H_{c}$, which we find to be of the order of 10-100 mT for realistic parameters. The instability develops into a stationary regime characterized by time periodic oscillations in the fundamental bending mode amplitude. We find that for nanotubes with large quality factors and a magnetic-field strength just above $H_{c}$ the frequency of the stationary vibrations is very close to the eigenfrequency of the fundamental mode. We also demonstrate that the magnetic field dependence of the time averaged voltage drop across the nanotube has a singularity at $H=H_{c}$. We discuss the possibility of using this phenomenon for the detection of nanotube vibrations.