Proximity Effect and Josephson Coupling in the SO(5) Theory of High-TcSuperconductivity

We consider proximity effect coupling in superconducting-antiferromagnetic-superconducting sandwiches using the recently developed $\mathrm{SO}\left(5\right)$ effective theory of high temperature superconductivity. We find that, for narrow junctions, the $A$ region acts like a strong superconductor, and that there is a critical junction thickness which depends on the effective $\mathrm{SO}\left(5\right)$ coupling constants and on the phase difference across the junction, at which the $A$ region undergoes a Freedericksz-like transition to a state which is intermediate between superconductor and antiferromagnet. For thick junctions, the current-phase relation is sinusoidal, as in standard SNS and SIS junctions, but for thin junctions it shows a sharp break in slope at the Freedericksz point.