Controlling the periodicity of the current-phase relation in multiterminal Josephson junctions

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. A critical characteristic of Josephson junctions is their current-phase relation. For SIS junctions, the current-phase relation is sinusioidal and 2π periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have non-sinusoidal current-phase relations that are still 2π periodic. We show here theoretically that a multi-terminal diffusive SNS Josephson junction with 4 superconducting contacts can show a current phase relation between two of the contacts that is a superposition of 2π and 4π periodic components. The relative strength between these two components can be controlled by the phase difference between the other two contacts, becoming 2π or 4π periodic for certain values of this phase difference. Potential experimental tests of this prediction will be discussed. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.

V. Chandrasekhar, Phys. Rev. B 112, 104508 (2025).