nu=1/2 quantum Hall effect in the Aharonov-Casher geometry in a mesoscopic ring

Details nu=1/2 quantum Hall effect in the Aharonov-Casher geometry in a mesoscopic ring nu=1/2 quantum Hall effect in the Aharonov-Casher geometry in a mesoscopic ring

1996-10-08

arxiv.org/abs/cond-mat/9610068v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

23 pages,14 included postscript figures, submitted to Phys. Rev. B

Scientific paper

10.1103/PhysRevB.55.13135

We study the effect of an electric charge in the middle of a ring of electrons in a magnetic field such as $\nu = 1/2$. In the absence of the central charge, a residual current should appear due to an Aharanov-Bohm effect. As the charge varies, periodic currents should appear in the ring. We evaluate the amplitude of these currents, as well as their period as the central charge varies. The presence of these currents should be a direct signature of the existence of a statistical gauge field in the $\nu=1/2$ quantum Hall effect. Numerical diagonalizations for a small number of electrons on the sphere are also carried out. The numerical results up to 9 electrons are qualitatively consistent with the mean field picture.

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