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A Mean Field Theory for the Quantum Hall Liquid. II --- The Vortex Solution

Kenzo Ishikawa·Nobuki Maeda
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Abstract

In the Fractional Quantum Hall state, we introduce a bi-local mean field and get vortex mean field solutions. Rotational invariance is imposed and the solution is constructed by means of numerical self-consistent method. It is shown that vortex has a fractional charge, a fractional angular momentum and a magnetic field dependent energy. In $ν=1/3$ state, we get finite energy gap at $B=10,15,20[T]$. We find that the gap vanishes at $B=5.5[T]$ and becomes negative below it. The uniform mean field becomes unstable toward vortex pair production below $B=5.5[T]$.

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Kenzo Ishikawa, Nobuki Maeda. 1993-06-04. A Mean Field Theory for the Quantum Hall Liquid. II --- The Vortex Solution. https://doi.org/10.1143/ptp%2F91.2.237

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