Frustration in d-wave Superconducting Circuits: $\pi$-Ring Behaviour
  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 superconductors and demonstrate the existence of spontaneous currents by direct self-consistent solutions to the Bogoliubov de Gennes equations. We show that the current has a topological origin due to the frustration of the d-wave order parameter, which is only partially explained by the Sigrist-Rice tunneling formula. 
J.J. Hogan-O'Neill, J.F. Annett, and A.M. Martin