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

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

1993-04-26

arxiv.org/abs/cond-mat/9304043v2

Prog. Theor. Phys. Vol. 91 (1994) 237

Physics

Condensed Matter

16pages,EPHOU 93-001,phyzzx

Scientific paper

10.1143/PTP.91.237

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 $\nu=1/3$ 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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