Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction

TL;DR

This paper investigates how the Josephson junction behavior changes in an interacting impurity system with superconducting leads, revealing the loss of pi-junction behavior as bound states shift above the Fermi level.

Contribution

It introduces a generalized non-crossing approximation including Andreev reflection to study impurity spectral functions in superconducting junctions, highlighting phase-dependent resonance behavior.

Findings

Sub-gap resonance shows strong phase dependence with a minimum at phase π.

Pi-junction behavior disappears when bound states move above the Fermi energy.

The study connects bound state energies with the loss of pi-junction behavior.

Abstract

Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where $\Delta$ and $T_K$ are comparable, we find that the position of the sub-gap resonance in the impurity spectral function develops a strong anomalous phase dependence-- its energy is a minimum when the phase difference between the superconductors is equal to $\pi$. Calculating the Josephson current through the impurity, we find that $\pi$-junction behaviour is lost as the position of the bound-state moves above the Fermi energy.