Knight Shift and Leading Superconducting Instability From Spin Fluctuations in Sr2RuO4

TL;DR

This paper investigates the possible superconducting pairing states in Sr2RuO4 using microscopic theory, considering recent NMR data, and predicts how the Knight shift varies with temperature for different pairing symmetries.

Contribution

It provides a comprehensive phase diagram of pairing states in Sr2RuO4, highlighting the dominance of even-parity singlet solutions and the conditions favoring triplet states, with predictions for Knight shift behavior.

Findings

Even-parity singlet solutions dominate large phase diagram regions.

Spin-orbit coupling can favor near-nodal triplet states.

Near-degeneracy of s' and d-wave solutions suggests possible time-reversal symmetry breaking state.

Abstract

Recent nuclear magnetic resonance studies [A. Pustogow {\it et al.}, arXiv:1904.00047] have challenged the prevalent chiral triplet pairing scenario proposed for Sr$_2$RuO$_4$. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin-fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band-structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the $\gamma$ band to the van Hove points. A surprising near-degeneracy of the nodal $s^\prime$- and $d_{x^2-y^2}$-wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken $s^\prime+id_{x^2-y^2}$ pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.