Spin-charge co-operation in even-parity three dimensional nodal superconductivity in strained Sr₂RuO₄

We develop a three-tier ab initio technique to study the origin and nature of the pairing in Sr₂RuO₄. The technique starts with the quasi-particle self consistent GW (QSGW) approximation to build a reference hamiltonian, augment it with dynamical mean field theory (DMFT) to add spin fluctuations left out of QSGW, and also generate the vertices entering into spin, charge, and pairing susceptibilities. Finally we solve multi-orbital Bethe-Salpeter equations to calculate these properties in both strained and unstrained single crystals. We identify what leads to the recently observed dependence of T_c on strain and also gain insights into what limits it. We find a one-to-one correspondence between T_c and the coherence and intensity of the spin susceptibility under application of strain. Finally, we establish connections between spin fluctuations and superconducting pairing symmetries in Sr₂RuO₄, and dimensionality of the fluctuations associated with these degrees of freedom.