Open AccessA Mean Field Theory for the Quantum Hall Liquid. II: The Vortex Solution
Author(s) -
Kenzo Ishikawa,
Nobuhiro Maeda
Publication year - 1994
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp/91.2.237
Subject(s) - physics , vortex , quantum hall effect , angular momentum , magnetic field , charge (physics) , field (mathematics) , quantum mechanics , condensed matter physics , fractional quantum hall effect , mean field theory , composite fermion , quantum electrodynamics , quantum spin hall effect , mechanics , mathematics , pure mathematics
In the Fractional Quantum Hall state, we introduce a bi-local mean field andget vortex mean field solutions. Rotational invariance is imposed and thesolution is constructed by means of numerical self-consistent method. It isshown that vortex has a fractional charge, a fractional angular momentum and amagnetic field dependent energy. In $\nu=1/3$ state, we get finite energy gapat $B=10,15,20[T]$. We find that the gap vanishes at $B=5.5[T]$ and becomesnegative below it. The uniform mean field becomes unstable toward vortex pairproduction below $B=5.5[T]$.Comment: 16pages,EPHOU 93-001,phyzz
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