The Meissner effect is analyzed in the Josephson junction predicted recently for a certain double-layer quantum Hall system. As a result of the Josephson current the magnetic field parallel to the layers is squeezed into a sine-Gordon vortex with the flux quantized in the unit of 2{π}/e. A distinctive feature of the vortex is the appearance of an electric potential well perpendicular to the magnetic field within the layers. We also estimate the maximum strength of the parallel magnetic field which can be expelled outside the junction.
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Ezawa et al. (1993) studied this question.
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