Measuring geometric phases of scattering states in nanoscale electronic devices

We show how a quantum property, a geometric phase, associated with scattering states can be exhibited in nanoscale electronic devices. We propose an experiment to use interference to directly measure the effect of this geometric phase. The setup involves a double-path interferometer, adapted from that used to measure the phase evolution of electrons as they traverse a quantum dot (QD). Gate voltages on the QD could be varied cyclically and adiabatically, in a manner similar to that used to observe quantum adiabatic charge pumping. The interference due to the geometric phase results in oscillations in the current collected in the drain when a small bias across the device is applied. We illustrate the effect with examples of geometric phases resulting from both Abelian and non-Abelian gauge potentials.