A recent study has investigated the accuracy with which currents in multiterminal Josephson junctions can be described by summing pairwise interactions between their terminals. These junctions, which couple three or more superconductors via a weak link, are of great interest for their potential to host topological Andreev bands, multi-pair supercurrents, and as tunable circuit elements. The research compares exact currents, obtained from a microscopic scattering model for planar junctions, with the best pairwise approximation, which allows for arbitrary nonsinusoidal couplings.

The results show that, although pairwise terms capture nearly all of the energy variation in ensembles of disordered three- and four-terminal junctions, the median current error ranges from 8.0% to 21.2%. This error is approximately twice the energy error, because currents more strongly weight the multiterminal harmonics. The study extended to designed devices with up to sixteen terminals. A key mechanism controlling this error has been identified: the presence of a normal-region mode near the Fermi level that couples to three or more terminals produces large nonpairwise currents. Detuning this mode with a gate suppresses these currents.

Finite-gap calculations in two clean devices confirm a drop in error from tens of percent near resonance to below one percent. An analytic single-level model provides sufficient detuning for pairwise accuracy, regardless of the terminal count. This suggests that planar junctions inherit the resonant and cotunneling regimes known from quantum dots, and that normal-state properties can identify the mode that distinguishes between them.

This finding is crucial for the design and understanding of quantum devices based on multiterminal Josephson junctions, as it allows for the prediction and control of nonpairwise current phenomena. The ability to tune these effects with a gate opens new avenues for engineering supercurrents and exploring complex quantum phenomena in these systems.