Shadowed triplet pairings in Hund's metals with spin-orbit coupling

TL;DR

This paper explores how spin-orbit coupling influences unconventional interorbital pairing in Hund's metals, revealing a hidden triplet pairing state called 'shadowed triplet' with potential implications for understanding Sr2RuO4.

Contribution

It introduces the concept of shadowed triplet pairing in Hund's metals, analyzing how momentum-dependent SOC stabilizes novel pairing symmetries like s+id_{xy} in Sr2RuO4.

Findings

Identification of shadowed triplet pairing as a hidden interorbital pairing state.

Derivation of SOC forms with d-wave symmetry from microscopic models.

Stabilization of s+id_{xy} pairing state under certain SOC parameters.

Abstract

Hund's coupling in multiorbital systems allows for the possibility of even-parity orbital-antisymmetric spin-triplet pairing, which can be stabilized by spin-orbit coupling (SOC). While this pairing expressed in the orbital basis is uniform and spin-triplet, it appears in the band basis as a pseudospin-singlet, with the momentum dependence determined by the SOC and the underlying triplet character remaining in the form of interband pairing active away from the Fermi energy. Here, we examine the role of momentum-dependent SOC in generating nontrivial pairing symmetries, as well as the hidden triplet nature associated with this interorbital pairing, which we dub a "shadowed triplet". Applying this concept to Sr$_{2}$RuO$_{4}$, we first derive several forms of SOC with $d$-wave form factors from a microscopic model, and subsequently we show that for a range of SOC parameters, a pairing state with $s+id_{xy}$ symmetry can be stabilized. Such a pairing state is distinct from pure spin-singlet and -triplet pairings due to its unique character of pseudospin-energy locking. We discuss experimental probes to differentiate the shadowed triplet pairing from conventional pseudospin-triplet and -singlet pairings.