  We demonstrate the physical principles for the construction of a nanometer
sized magnetoresistance device based on the Aharonov-Bohm effect. The proposed
device is made of a short single-walled carbon nanotube (SWCNT) placed on a
substrate and coupled to a tip. We consider conductance due to motion of
electrons along the circumference of the tube (as opposed to motion parallel to
its axis). We find that the circumference conductance is sensitive to magnetic
fields threading the SWCNT due to the Aharonov-Bohm effect, and show that by
retracting the tip, so that its coupling to the SWCNT is reduced, very high
sensitivity to the threading magnetic field develops. This is due to the
formation of a narrow resonance through which the tunneling current flows.
Using a bias potential the resonance can be shifted to low magnetic fields,
allowing the control of conductance with magnetic fields of the order of 1
Tesla.
