Nodal gaps from local interactions in Sr$_2$RuO$_4$

Sr$_2$RuO$_4$ has been under intensive scrutiny over the past years after new NMR measurements unveiled that the superconducting state might be a spin singlet. One of the best order parameter candidates in light of these new experiments is a chiral d-wave state with $d_{xz}+id_{yz}$ symmetry. This order parameter has been overlooked given the strong two-dimensional character of the normal state electronic structure. Recently, a phenomenological proposal based on local interactions with a three-dimensional electronic structure showed that a chiral d-wave state can be stable in Sr$_2$RuO$_4$ once momentum-dependent spin-orbit coupling is properly taken into account. Here we discuss the origin of the nodes and dips in this order parameter as inherited from the normal state Hamiltonian, showing that a nodal gap can emerge out of purely local interactions and connect the presence of nodes with the superconducting fitness measure.