Charge Transport and Quantum Phase Transitions in Singlet Superconductor - Ferromagnet - Singlet Superconductor Junctions

TL;DR

This paper investigates how the Josephson current in a superconductor-ferromagnet-superconductor junction depends on magnetic and non-magnetic scattering, revealing non-analyticities, temperature-induced sign changes, and quantum phase transitions.

Contribution

It provides a detailed analysis of the dependence of Josephson current on scattering potentials and phase difference, identifying conditions for quantum phase transitions and current sign changes.

Findings

Critical current has non-analytic lines in (g, Z)-plane.

Josephson current can change sign with temperature without 0- transition.

Tuning phase difference induces a first-order quantum phase transition.

Abstract

We study the Josephson current, I_J, in a junction consisting of two s-wave superconductors that are separated by a ferromagnetic barrier possessing a magnetic and non-magnetic scattering potential, g and Z, respectively. We discuss the general dependence of I_J on g, Z, and the phase difference \phi between the two superconductors. Moreover, we compute the critical current, I_c for given g and Z, and show that it possesses two lines of non-analyticity in the (g, Z)-plane. We identify those regions in the (g, Z)-plane where the Josephson current changes sign with increasing temperature without a change in the relative phase between the two superconductors, i.e., without a transition between a 0 and \pi state of the junction. Finally, we show that by changing the relative phase \phi, it is possible to tune the junction through a first-order quantum phase transition in which the spin polarization of the two superconductors' combined ground state changes from < S_z > =0 to < S_z > =1/2.