Abstract
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. The vortex carries a flux which is determined by vanishing of the charge density of the electronic fluid due to the insulating region. The sign of the vorticity for a hole is opposite to the vorticity for adding additional electrons. The vorticity gives rise to non-commuting kinetic momenta. The two dimensional electron gas is described as 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 coordinate do not commute and 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. Using a Bosonized formulation of the two dimensional gas in the presence of insulating regions allows us to compute the rectified current. The proposed theory may explain the experimental results recently reported by J. Zhang et al.PACS numbers: 71.10.PM
Highlights
The topology of the ground state wave function plays a crucial role in determining the physical properties of a many-particle system
It is known that Fermions and Bosons obey different quantization rules, while the quantized Hall conductance [1] and the value of the spin-Hall conductivity are a result of non-commuting Cartesian coordinates [2]
The major result which occurs in the absence of the magnetic field is a change in sign of the rectified voltage when the microwave frequency varies from 1.46 GHz to 17.41 GHz
Summary
The topology of the ground state wave function plays a crucial role in determining the physical properties of a many-particle system These properties are revealed through the quantization rules. The phenomena of quantum pumping observed in one-dimensional electronic systems [3,4,5] is a result of a space-time cycle and can be expressed in the language of non-commuting frequency = i t and coordinate x = i k as shown in ref[6].
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