Josephson effect of superconductors with $J=3/2$ electrons

TL;DR

This paper theoretically investigates the Josephson effect in superconductors composed of $J=3/2$ electrons, revealing unique selection rules and the influence of interface properties and odd-frequency pairs.

Contribution

It introduces the study of Josephson effects and selection rules in $J=3/2$ electron superconductors, highlighting differences from conventional $S=1/2$ systems.

Findings

Selection rules are more restrictive for quintet states than for spin-triplet states.

Pseudospin-active interfaces significantly affect the Josephson selection rules.

Odd-frequency Cooper pairs influence the Josephson effect in these systems.

Abstract

The angular momentum of an electron is characterized well by pseudospin with $J=3/2$ in the presence of strong spin-orbit interactions. We study theoretically the Josephson effect of superconductors in which such two $J=3/2$ electrons form a Cooper pair. Within even-parity symmetry class, pseudospin-quintet pairing states with $J=2$ can exist as well as pseudospin-singlet state with $J=0$. We focus especially on the Josephson selection rule among these even-parity superconductors. We find that the selection rule between quintet states is severer than that between spin-triplet states formed by two $S=1/2$ electrons. The effects of a pseudospin-active interface on the selection rule are discussed as well as those of odd-frequency Cooper pairs generated by pseudospin dependent band structures.