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Frustration in d-wave Superconducting Circuits: $π$-Ring Behaviour

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

A closed superconducting circuit containing an odd number of $π$-junctions, a $π$-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.

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J. J. Hogan-O'Neill, J. F. Annett, A. M. Martin. 2000-06-02. Frustration in d-wave Superconducting Circuits: $π$-Ring Behaviour. https://arxiv.org/abs/cond-mat/0006033

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