Phase Diagram of Nickelate Superconductors Calculated by Dynamical Vertex Approximation

We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model, we identify the one-band Hubbard model for the Ni 3 dx2−y2 orbital plus a pocket around the A -momentum. The latter, however, merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from nominal Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by the experiment, indicate that the Γ pocket, Nd 4 f orbitals, oxygen 2 p , and the other Ni 3 d orbitals are not relevant in the superconducting doping regime. The physics is completely different if topotactic hydrogen is present or the oxygen reduction is incomplete. Then, a two-band physics hosted by the Ni 3 dx2−y2 and 3 d3z2−r2 orbitals emerges. Based on our minimal modeling, we calculated the superconducting T c vs. Sr-doping x phase diagram prior to the experiment using the dynamical vertex approximation. For such a notoriously difficult to determine quantity as T c , the agreement with the experiment is astonishingly good. The prediction that T c is enhanced with pressure or compressive strain has been confirmed experimentally as well. This supports that the one-band Hubbard model plus an electron reservoir is the appropriate minimal model.