Josephson Current in the Presence of a Precessing Spin

TL;DR

This paper investigates how a precessing spin affects the Josephson current between different types of superconductors, revealing conditions under which the current is modulated or suppressed.

Contribution

It demonstrates that the Josephson current is unaffected by spin precession in singlet superconductors but modulated in equal-spin-triplet superconductors, and identifies conditions for current suppression.

Findings

Josephson current is not modulated in singlet superconductors.

Current is modulated at twice the Larmor frequency in triplet superconductors.

No Josephson current occurs with direct exchange interaction between different spin-parity pairings.

Abstract

The Josephson current in the presence of a precessing spin between various types of superconductors is studied. It is shown that the Josephson current flowing between two spin-singlet pairing superconductors is not modulated by the precession of the spin. When both superconductors have equal-spin-triplet pairing state, the flowing Josephson current is modulated with twice of the Larmor frequency by the precessing spin. It was also found that up to the second tunneling matrix elements, no Josephson current can occur with only a direct exchange interaction between the localized spin and the conduction electrons, if the two superconductors have different spin-parity pairing states.