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.