Conductance oscillations in a multi-branch Andreev interferometer

The conductance, g(ø), of a comb-shaped N-branch Andreev interferometer is calculated as a function of the phase difference, ø, between the adjacent superconducting order parameters. In the ballistic regime, the scattering matrix theory predicts for the conductivity a typical N-branch interference pattern, that is, a 2π-periodic ø dependence with a fine oscillation of the period 2π/(N -1), while for a diffusive system with barriers between the vertices the quasiclassical circuit theory yields a simple 2π-periodic conductance regardless of N. With ensemble averaging in the scattering matrix theory, the fine oscillations get washed out, resulting in a simple π-periodic conductance. In star-shaped interferometers with all the N normal vertices merged into a single vertex, the conductance exhibits similar N-branch interference patterns regardless of whether the conduction is ballistic or diffusive or whether it is ensemble-averaged or not.