Roles of Electron Correlations in the Spin-Triplet Superconductivity of Sr2RuO4

TL;DR

This paper investigates the microscopic mechanisms behind spin-triplet superconductivity in Sr2RuO4, emphasizing the role of electron correlations and specific band contributions, challenging the idea that magnetic fluctuations are the primary cause.

Contribution

It demonstrates that electron correlations and vertex corrections favor spin-triplet p-wave pairing in Sr2RuO4, with the γ band playing a dominant role, and suggests superconductivity arises naturally from electron interactions.

Findings

Spin-triplet p-wave state is more stable than d-wave for moderate Coulomb interactions.

The γ band primarily drives the superconducting transition.

Vertex corrections significantly influence the momentum dependence of pairing.

Abstract

We discuss a microscopic mechanism of the spin-tiplet superconductivity in the quasi-two-dimensional ruthenium oxide Sr2RuO4 on the basis of two-dimensional three-band Hubbard model. We solve the linearized Eliashberg equation by taking into account the full momentum-frequency dependence of the order parameter for the spin-triplet and the spin-singlet states, and estimate the transition temperature as a function of the Coulomb integrals. The effective pairing interaction is expanded perturbatively with respect to the Coulomb interaction at the Ru sites up to the third order. As a result, we show that the spin-triplet p-wave state is more stable than the spin-singlet d-wave state for moderately strong Coulomb interaction. Our results suggest that one of the three bands, $\gamma$, plays a dominant role in the superconducting transition, and the pairing on the other two bands($\alpha$ and $\beta$) is induced passively through the inter-orbit couplings. The most significant momentum dependence for the p-wave pairing originates from the vertex correction terms, while the incommensurate antiferromagnetic spin fluctuations, which are observed in inelastic neutron scattering experiments, are expected to disturb the p-wave pairing by enhancing the d-wave pairing. Therefore we can regard the spin-triplet superconductivity in Sr2RuO4 as one of the natural results of the electron correlations, and cannot consider as a result of some strong magnetic fluctuations. We will also mention the normal Fermi liquid properties of Sr2RuO4.