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

TL;DR

This paper investigates Nambu-Goldstone modes and Josephson supercurrents in bilayer quantum Hall systems at filling factors 1 and 2, revealing their role in phase coherence and dissipationless transport.

Contribution

It introduces a theoretical analysis of phase coherence and supercurrents linked to Nambu-Goldstone modes in bilayer quantum Hall systems using Grassmannian formalism.

Findings

Identification of complex Nambu-Goldstone modes with linear dispersion

Demonstration of Josephson supercurrent induced by phase coherence

Impact on Hall resistance in bilayer quantum Hall systems

Abstract

An interlayer phase coherence develops spontaneously in the bilayer quantum Hall system at the filling factor $\nu =1$. 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 $\nu =2$. 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 $\nu=1,2$, by employing the Grassmannian formalism.