Frustration in d-wave Superconducting Circuits: $\pi$-Ring Behaviour

J. J. Hogan-O'Neill, J. F. Annett, A. M. Martin

A closed superconducting circuit containing an odd number of $\pi$-junctions, a $\pi$-ring, has a finite current in the ground state. We explicitly construct such rings for d-wave supe…