Spin Supercurrent in the Canted Antiferromagnetic Phase

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The spin and layer (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 Goldstone mode describing such a combined degree of freedom. In the zero tunneling-interaction limit (ΔSAS→ 0), its phase field provokes a supercurrent carrying both spin and charge within each layer. The Hall resistance is predicted to become anomalous precisely as in the ν=1 bilayer system in the counterflow and drag experiments. Furthermore, it is shown that the total current flowing in the bilayer system is a supercurrent carrying solely spins in the counterflow geometry. It is intriguing that all these phenomena occur only in imbalanced bilayer systems.