Josephson effect of superconductors with J = 3 2 electrons

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 two such 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 states 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 more severe than that between spin-triplet states formed by two S = ½ 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.