  The effect of a magnetic field on Josephson current has been studied for a
superconductor/normal-metal/superconductor (SNS) system, where N is a
two-dimensional electron gas in a confining potential. It is found that the
dependence of Josephson currents on the magnetic field are sensitive to the
width of the normal metal. If the normal metal is wide and contains many
channels (subbands), the current on a weak magnetic field shows a dependence
similar to a Fraunhofer-pattern in SIS system and, as the field gets strong, it
shows another type of oscillatory dependence on the field resulting from the
Aharonov-Bohm interference between the edge states. As the number of channels
decreases (i.e. normal metal gets narrower), however, the dependence in the
region of the weak field deviates from a clear Fraunhofer pattern and the
amplitude of the oscillatory dependence in the region of the strong field is
reduced.
