Scattering-matrix approach to the theory of Josephson transport in mesoscopic multiterminal nodes

•The scattering-matrix approach was applied for multiterminal Josephson nodes.•The current-phase relations were calculated for a three-terminal system.•The applications of our results and typical experimental examples were discussed.

Within the Bogoliubov–de Gennes theory we have studied the transport properties of disordered Josephson systems with several superconducting electrodes weakly coupled through a normal region. The scattering-matrix approach has been applied for arbitrary geometries of the normal region to analyze the quasi-particle spectra and current-phase relations (CPRs). The dependence of CPRs on the system geometry and its lengths reveals itself in the coefficients of the scattering matrix in the connecting normal area. This approach is applicable to mesoscopic superconducting structures with a normal weak link which appears to be small compared to the superconducting coherence length. The possible applications of our results and typical experimental examples have been discussed.