Intertwined superconductivity and orbital selectivity in a three-orbital Hubbard model for the iron pnictides

We study a three-orbital Hubbard-Kanamori model relevant for iron-based superconductors using variational wave functions explicitly including spatial correlations and electron pairing. We span the nonmagnetic sector from filling $n=4$, which is representative of undoped iron-based superconductors, to $n=3$, where a Mott insulating state with each orbital at half filling is found. In the strong-coupling regime, when the electron density is increased, we find a spontaneous differentiation between the occupation of $d_{xz}$ and $d_{yz}$ orbitals, leading to an orbital-selective state with a nematic character that becomes stronger at increasing density. One of these orbitals stays half-filled for all densities while the other one hosts (together with the $d_{xy}$ orbital) the excess of electron density. Most importantly, in this regime long-range pairing correlations appear in the orbital with the largest occupation. Our results highlight a strong link between orbital-selective correlations, nematicity, and superconductivity, which requires the presence of a significant Hund’s coupling.