Rectified Voltage Induced by a Microwave Field in a Confined Two-Dimensional Electron Gas with a Mesoscopic Static Vortex

We investigate the effect of a microwave field on a confined two dimensional electron gas which contains an insulating region comparable to the Fermi wavelength. The insulating region causes the electron wave function to vanish in that region. We describe the insulating region as a static vortex, which gives rise to non-commuting kinetic momenta. The two-dimensional electron gas is described as a fluid with a density which obeys the Fermi-Dirac statistics. The presence of the confinement potential gives rise to vanishing kinetic momenta in the vicinity of the classical turning points. As a result, the Cartesian coordinates do not commute. The non-commutativity of coordinates gives rise to a Hall current which, in the presence of a modified Fermi-Surface caused by the microwave field, results in a rectified voltage. The proposed theory may explain the experimental results recently reported by J. Zhang et al.