Orbital-order as the driving mechanism for superconductivity in ruthenates

Several materials transition from an insulating to a superconducting state by reducing the strength of the electron-phonon coupling associated with charge and bond orderings provided that the coupling remains strong enough to produce Cooper pairs. While the Jahn-Teller effect is at the core of a strong electron-phonon coupling producing insulating states and orbital and bond orderings, its implication in superconductivity remains unobserved. Here, with parameter-free first-principles calculations, we reveal that superconductivity in A₂RuO₄ (A = Sr, Ca) emerges due to an electron-phonon mechanism associated with the proximity of an orbital and bond-ordered phase. The model predicts critical temperatures T_c of 0.5-1.65 K in bulk Sr₂RuO₄ and 63-73 K in pressured Ca₂RuO₄, in agreement with experiments. Our results suggest that phonons strongly coupled to electrons, such as those involved in charge disproportionation or Jahn-Teller effects and inducing band gaps in various oxides, could also serve as mediators of Cooper pairs in metallic phases.