Interlayer coupling and $p$-wave pairing in strontium ruthenate

On the basis of a three-orbital model and an effective attractive interaction between electrons, we investigate the possible superconducting states, with p- and f-wave internal symmetries, of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4.$ For an orbital-dependent interaction which acts between in-plane and out-of-plane nearest-neighbor ruthenium atoms, we find a state for which the gap in the quasiparticle spectra has nodes on the $\alpha$ and $\beta$ sheets of the Fermi surface, but which is complex with no nodes on the $\gamma$ sheet. We show that this state is consistent with the available experimental data. In particular, we present the results of our calculations of the specific heat and penetration depth as functions of temperature.