Realization of the $\pi$-state in junctions formed by multi-band superconductors with a spin-density-wave

TL;DR

This paper investigates the Josephson effect in multi-band superconductors with spin-density-wave order, revealing conditions for $\

Contribution

It introduces a model for Josephson junctions involving multi-band superconductors with SDW, highlighting the impact of magnetic order and complex tunneling elements on the $\

Findings

Realization of $\

Dependence of Josephson current on SDW orientation

Appearance of a new term with complex tunneling matrix elements

Abstract

Using a simple model of multi-band superconductors, which can be applied in particular to Fe\nobreakdash-based pnictides, we calculate the Josephson current $I_{\text{J}}$ in a tunnel junction composed by such superconductors. We employ the tunneling Hamiltonian method and quasiclassical Green's functions. We study both the case of coexistence of the superconducting ($\Delta $) and magnetic (SDW---spin density wave) order parameters and the case when only the superconducting order parameter exists. We show that the current $I_{\text{J}}$ depends on the mutual orientation of magnetization of the SDW in the case of non-ideal nesting when the coexistence of superconducting and magnetic order parameters is possible as it takes place in Fe\nobreakdash-based pnictides. It is found that the realization of the $\pi$\nobreakdash-junction is possible in both cases. We compare our results for multi-band superconductors without the SDW with those obtained earlier and find that they coincide if the tunneling matrix elements are real. If these elements are complex, a new term appears in the formula for the Josephson critical current.