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

TL;DR

This paper investigates the influence of a central electric charge on a mesoscopic ring exhibiting the ν=1/2 quantum Hall effect, revealing periodic currents as signatures of a statistical gauge field.

Contribution

It provides a theoretical and numerical analysis of how a central charge induces observable currents, linking them to the presence of a statistical gauge field in the ν=1/2 quantum Hall regime.

Findings

Periodic currents depend on the central charge value.

Numerical results with up to 9 electrons support the mean field model.

Presence of these currents indicates a statistical gauge field in the system.

Abstract

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.