  Mechanical displacements of a nanoelectromechanical system (NEMS) shift the
electron trajectories and hence perturb phase coherent charge transport through
the device. We show theoretically that in the presence of a magnetic feld such
quantum-coherent displacements may give rise to an Aharonov-Bohm-type of
effect. In particular, we demonstrate that quantum vibrations of a suspended
carbon nanotube result in a positive nanotube magnetoresistance, which
decreases slowly with the increase of temperature. This effect may enable one
to detect quantum displacement fluctuations of a nanomechanical device.
