Leading superconducting instabilities in three-dimensional models for Sr2RuO4

TL;DR

This paper systematically investigates the leading superconducting instabilities in Sr2RuO4 using a realistic three-dimensional model, revealing dominant nodal even-parity states and analyzing their stability with respect to various interactions and spin-orbit couplings.

Contribution

It provides a comprehensive analysis of superconducting instabilities in Sr2RuO4 considering 3D Fermi surfaces, spin-orbit coupling, and fluctuation exchange mechanisms, identifying the most stable pairing states.

Findings

Nodal even-parity s' and d_{x^2-y^2} states are dominant.

The d_{xz}/d_{yz} state can be stabilized under certain conditions.

Full fluctuation exchange vertex favors other solutions over E_g pairing.

Abstract

The superconductor Sr2RuO4 has been the subject of enormous interest over more than two decades, but until now the form of its order parameter has not been determined. Since groundbreaking NMR experiments revealed that the pairs are of dominant spin-singlet character, attention has focused on time-reversal symmetry breaking linear combinations of $s$-, $d$- and $g$-wave one-dimensional (1D) irreducible representations. However, a state of the form $d_{xz}+id_{yz}$ has also been proposed. We present a systematic study of the stability of various superconducting candidate states, assuming that pairing is driven by the fluctuation exchange mechanism, including a realistic three-dimensional Fermi surface, full treatment of both local and non-local spin-orbit couplings, and a wide range of interaction parameters $U,J,U',J'$. The leading superconducting instabilities are found to exhibit nodal even-parity $A_{1g} (s')$ or $B_{1g} (d_{x^2-y^2})$ symmetries, similar to the findings in two-dimensional models without longer-range Coulomb interaction which tends to favor $d_{xy}$ over $d_{x^2-y^2}$. Within the so-called Hund's coupling mean-field pairing scenario, the $E_g (d_{xz}/d_{yz})$ solution can be stabilized for large $J$ and specific forms of the spin-orbit coupling, but for all cases studied here the eigenvalues of other superconducting solutions are significantly larger when the full fluctuation exchange vertex is included in the pairing kernel. Additionally, we compute the spin susceptibility in relevant superconducting candidate phases and compare to recent neutron scattering and NMR Knight shift measurements.