Evening out the spin and charge parity to increase T$_c$ in unconventional superconductor Sr_{2}RuO_{4}

Unconventional superconductivity in Sr$_{2}$RuO$_{4}$ has been intensively studied for decades. The origin and nature of the pairing continues to be widely debated, in particular, the possibility of a triplet origin of Cooper pairs. However, complexity of Sr$_{2}$RuO$_{4}$ with multiple low-energy scales, involving subtle interplay among spin, charge and orbital degrees of freedom, calls for advanced theoretical approaches which treat on equal footing all electronic effects. Here we develop a novel approach, a detailed \emph{ab initio} theory, coupling quasiparticle self-consistent \emph{GW} approximation with dynamical mean field theory (DMFT), including both local and non-local correlations. We report that the superconducting instability has multiple triplet and singlet components. In the unstrained case the triplet eigenvalues are larger than the singlets. Under uniaxial strain, the triplet eigenvalues drop rapidly and the singlet components increase. This is concomitant with our observation of spin and charge fluctuations shifting closer to wave-vectors favoring singlet pairing in the Brillouin zone. We identify a complex mechanism where charge fluctuations and spin fluctuations co-operate in the even-parity channel under strain leading to increment in $T_c$, thus proposing a novel mechanism for pushing the frontier of $T_c$ in unconventional `triplet' superconductors.