Identifying the pairing mechanism in strontium ruthenate via renormalization

The superconducting state of strontium ruthenate Sr${}_2$RuO${}_4$ has mysteriously succeeded in defying any valid theory and the identification of its gap function for more than twenty years. Even the results of different experimental techniques seem to contradict each other when trying to pinpoint the order parameter. Former theories aiming at a description in terms of a time-reversal symmetry broken (chiral) state were experimentally disproven by the non-existence of edge currents. Our calculations are based on a more complete single-particle model that does not only incorporate the on-site spin-orbit interaction but also more extended non-local spin-orbit coupling terms which are evaluated in all d-orbitals. Using a combined weak-coupling and functional renormalization group approach we integrate out the high-energy degrees of freedom to identify the gap functions for a set of realistic interaction parameters. Motivated by recent experimental results showing a strong increase of the critical temperature under uniaxial pressure, we also explore the consequences of breaking the lattice symmetry $D_{4h}$ down to $D_{2h}$.