Perturbation theory of a zero-pi transition in a superconducting quantum dot system

Abstract: An interplay between the on-site Coulomb repulsion and the superconducting order in a single-level quantum dot attached to two superconducting leads is studied via the perturbation expansion in the interaction strength. This system displays interesting quantum effects at low temperatures. We focus on the so-called zero-pi transition marked by the reversal of the sign of the Josephson current. The results show nearly perfect agreement with the (numerically exact) NRG calculations for the position of the phase boundary at which the Andreev bound states reach the Fermi energy.