Conventional superconductor/insulator/superconductor (SIS) Josephson junctions, devices where two superconductors are separated by a tunnel barrier, are technologically important as elements in quantum circuits, particularly with their key role in superconducting qubits. An important characteristic of Josephson junctions is the relation between the supercurrent $I_s$ and the phase difference $\phi$ between them. For SIS junctions, the current-phase relation is sinusoidal and $2\pi$ periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have nonsinusoidal current-phase relations that are still $2\pi$ periodic. We show here that a multiterminal diffusive SNS Josephson junction with four superconducting contacts can show a current phase relation between two of the contacts that is a superposition of $2\pi$ and $4\pi$ periodic components whose relative strength is controlled by the phase difference between the other two contacts, becoming $2\pi$ or $4\pi$ periodic for certain values of this phase difference. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.

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• Proximity effect
• Superconductivity
• Josephson junctions
• Green's function methods
• Usadel equation