Josephson effect in spin-singlet superconductor/ferromagnetic insulator/spin-triplet superconductor junctions with helical $p$-wave states

TL;DR

This paper investigates the Josephson effect in junctions between spin-singlet and spin-triplet superconductors with helical p-wave states, revealing the conditions for different current-phase relations and their dependence on magnetization orientation.

Contribution

It demonstrates that both sine and cosine current-phase relations can occur in such junctions, depending on magnetization components and gap symmetries, providing new insights into their interplay.

Findings

Both $ ext{sin}\phi$ and $ ext{cos}\phi$-type currents exist regardless of gap symmetry.

Magnetization components parallel to crystallographic axes are essential for these currents.

Josephson current sign reversal depends on magnetization rotation.

Abstract

We study the Josephson effect in spin-singlet superconductor/helical $p$-wave superconductor junctions with a ferromagnetic barrier using the quasiclassical Green function method. It is found that both $\sin{\phi}$-type and $\cos{\phi}$-type current-phase relations always exist, irrespective of the gap symmetries in superconductors. The indispensable condition for the $\sin{\phi}$-type and $\cos{\phi}$-type current is that the magnetization must have a component parallel to the crystallographic $a$ or $b$ axis, which is distinct from the case of $p$-wave superconductor described by a $\vect{d}$-vector with a uniform direction. The relation between the condition and the symmetries of the gap functions is analysed. We investigate in detail the symmetries and the sign reversal of the Josephson current when the magnetization is rotated.