0–π Transition and Second Harmonic Generation in Diffusive S/F/S Josephson Junction

Abstract

We theoretically investigate the Josephson effect in a Josephson junction consisting of a ferromagnetic layer sandwiched between two superconductors. Using the quasiclassical Green’s function method and perturbative calculations, we derive analytical expressions for the first harmonic Josephson current (FHJC) and the second harmonic Josephson current (SHJC) in the diffusive regime. Both components exhibit damped oscillatory behavior as functions of the ferromagnetic layer thickness, accompanied by sign changes, indicating the occurrence of 0-π transitions. The analytical results clarify that the oscillation period of the SHJC is half that of the FHJC, while its damping rate is twice as large. These findings suggest that a thin ferromagnetic layer is essential to realize a significantly large SHJC.