Higher angular momentum pairings in interorbital shadowed-triplet superconductors: Application to Sr${}_2$RuO${}_4$

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.

arXiv comment13 pages, 3 figures

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• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• In-plane magnetic penetration depth in Sr${}_2$RuO${}_4$: muon-spin rotation/relaxation study
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• Spin susceptibility for orbital-singlet Cooper pair in the three-dimensional Sr${}_2$RuO${}_4$ superconductor
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• Spin-orbit-coupled superconductivity with spin-singlet non-unitary pairing
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