Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr$_{2}$RuO$_{4}$

TL;DR

This paper explores how higher angular momentum pairings, such as d- and g-wave, can emerge in multiorbital superconductors with spin-orbit coupling, specifically applied to Sr$_{2}$RuO$_{4}$, revealing a rich competition of pairing states.

Contribution

It demonstrates how momentum-dependent spin-orbit coupling can induce higher angular momentum pairings in interorbital shadowed-triplet superconductors, with application to Sr$_{2}$RuO$_{4}$.

Findings

Presence of d- and g-wave pairings in Sr$_{2}$RuO$_{4}$ when spin-orbit coupling parameters are tuned.

Identification of a d+ig pairing state arising from increased d-wave character of spin-orbit coupling.

Competition among multiple pairing states influenced by spin-orbit coupling parameters.

Abstract

Even-parity interorbital spin-triplet pairing emerges as an intriguing candidate in multiorbital superconductors with significant Hund's and spin-orbit coupling. Within such a state, the pairing is dominated by the intraband pseudospin-singlet component via the spin-orbit coupling, distinguishing it from a pure spin triplet and motivating the name, shadowed triplet. With atomic spin-orbit coupling, it was shown that this pairing exhibits an anisotropic $s$-wave character, while higher angular momentum pairing symmetries such as $d$- or $g$-wave have been proposed based on phenomenological analyses in candidate systems. A natural question is then whether higher angular momentum pairings may arise with this form of spin-triplet pairing. Here, we examine the interplay between spin-orbit coupling and the electronic dispersions in correlated metals and demonstrate how they can be realized. We apply this idea to Sr$_{2}$RuO$_{4}$ and determine the competition among different pairing states as multiple spin-orbit coupling parameters are tuned. The presence of both $d$- and $g$-wave pairings, including a $d+ig$ state, are found when momentum-dependent spin-orbit coupling with $d$-wave character is increased. Implications of the theory and future directions are also discussed.