Nambu-Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system

Abstract

An interlayer phase coherence develops spontaneously in the bilayer quantum Hall system at the filling factor $ν=1$. On the other hand, the spin and pseudospin degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor $ν=2$. There emerges a complex Nambu-Goldstone mode with a linear dispersion in the zero tunneling-interaction limit for both cases. Then its phase field provokes a Josephson supercurrent in each layer, which is dissipationless as in a superconductor. We study what kind of phase coherence the Nambu-Goldstone mode develops in association with the Josephson supercurrent and its effect on the Hall resistance in the bilayer quantum Hall system at $ν=1,2$, by employing the Grassmannian formalism.

43 pages, 5 figures. arXiv admin note: text overlap with arXiv:1207.0003, arXiv:1211.0384