Theoretical Studies of Unconventional Superconductivity in Materials with Strong Electronic Correlations

We use a combination of Density Functional Theory and Dynamical Mean Field Theory (DFT+DMFT) to study electronic correlations in unconventional superconductors, with a focus on nickelate analogs of cuprate superconductors. We study the infinite layer nickelate superconductor NdNiO₂ in parallel with the isostructural CaCuO₂. Our results point to superconductivity in the nickelate being cupratelike, with correlations dominated by a hybrid Ni-_{²-²} and O- band, and with the extra bands not contributing substantially to the superconducting state. We find that the infinite layer nickelate NdNiO₂ and the trilayer nickelate Pr₄Ni₃O₈ are virtually identical in terms of correlation physics when compared at the same chemical doping, despite the differences in Fermiology, indicating that the number of layers can stand in for chemical doping for some properties related to electronic correlations. We find that as opposed to in narrow window DFT+DMFT, in wide window DFT+DMFT the choice of downfolding procedure leads to very different results. This is an important ambiguity in the method that must be resolved or the method is incomplete by itself. We also study Sr₂MoO₄ in parallel with the Hund's superconductor Sr₂RuO₄, and find that Sr₂MoO₄ is a particle-hole dual of Sr₂RuO₄ but without the van Hove singularity at the Fermi level, which disentangles the influence of the van Hove singularity from Hund's physics. We show that Sr₂MoO₄ has a characteristic Hund's peak on the occupied of the spectral function, indicating that the peak should be observable by photoemission experiments