We compute and compare even-and odd-parity superconducting order parameters of strontium ruthenate (Sr2RuO4) in the limit of weak interactions, resulting from a fully microscopic threedimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity dwave order are favored for smaller and larger values of the Hund's coupling parameter J, respectively. Both orders are found compatible with specific heat data and the recently-reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al. arXiv:1904.00047 (2019]. The chiral p-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.
We study a three-dimensional single-band repulsive Hubbard model at weak coupling. We establish the superconducting phase diagram in the parameter space of the chemical potential and the out-of-plane hopping strength. The model continuously connects the Hubbard model in two and three dimensions. We confirm previously-established results in these limits, and identify a rich structure of competing order parameters in between. Specifically, we find five types of p-and dwave orders. In several regions of the phase diagram, even when the Fermi surface is a corrugated cylinder, the ground state is a time-reversal-symmetry-breaking superconductor with nodes, i.e. a Weyl superconductor.
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