  The Sagnac effect is an important phase coherent effect in optical and atom
interferometers where rotations of the interferometer with respect to an
inertial reference frame result in a shift in the interference pattern
proportional to the rotation rate. Here we analyze for the first time the
Sagnac effect in a mesoscopic semiconductor electron interferometer. We include
in our analysis Rashba spin-orbit interactions in the ring. Our results
indicate that spin-orbit interactions increase the rotation induced phase
shift. We discuss the potential experimental observability of the Sagnac phase
shift in such mesoscopic systems.
