Real-space geometric curvature in magnetic thin films introduces a controllable mechanism for tailoring the pathways of superconducting steady-state Josephson currents via the proximity effect. We present a generalized Green's function method for calculating diffusive transport in arbitrarily curved surfaces, and show how the competing mechanisms of curvature and distance regulate conversion between different superconducting pairings in a proximity-coupled ferromagnet. We show how this dictates the distribution of current density, with the possibility of curvature-controlled current density manipulation, induced eddy currents, and current reversal.

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• Magnetism
• Odd-frequency superconductivity
• Proximity effect
• Quantum fields in curved spacetime
• Spintronics
• Superconductivity
• Josephson junctions
• Twisted films
• Green's function methods
• Methods in superconductivity
• Usadel equation