Conductance Oscillations in A Multi-Branch Andreev Interferometer

The conductance, g(phi), of a comb-shaped N-branch Andreev interferometer is calculated as a function of the phase difference, phi, 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 2 pi-periodic phi dependence with a fine oscillation of the period 2 pi/(N - 1), while for a diffusive system with barriers between the vertices the quasiclassical circuit theory yields a simple 2 pi-periodic conductance regardless of N. With ensemble averaging in the scattering matrix theory, the fine oscillations get washed out, resulting in a simple pi-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.