Prog. Theor. Phys. Vol. 91 No. 2 (1994) pp. 237-249

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A Mean Field Theory for the Quantum Hall Liquid. II

— The Vortex Solution —

Kenzo Ishikawa and Nobuki Maeda

Department of Physics, Hokkaido University, Sapporo 060

(Received April 12, 1993)

Abstract:

In the Fractional Quantum Hall state, we get vortex mean field solutions. Imposing rotational invariance, we construct the solution by means of numerical self-consistent method. It is shown that the 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 the vortex pair production below B = 5.5[T] if the fluctuations are ignored.

URL : http://ptp.ipap.jp/link?PTP/91/237/
DOI : 10.1143/PTP.91.237

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Citing Article(s) :

Progress of Theoretical Physics Vol. 93 No. 3 (1995) pp. 503-518 :
Charged and Neutral Vortex Excitations in a Mean Field Theory for the Fractional Quantum Hall Effect

Nobuki Maeda
Progress of Theoretical Physics Vol. 97 No. 3 (1997) pp. 507-525 :
Flux State in von Neumann Lattices and the Fractional Hall Effect

Kenzo Ishikawa and Nobuki Maeda