Universal quasidegenerate orbital origin of two-dome phases in iron pnictide superconductors

A series of experiments revealed that novel bipartite magnetic and superconducting (SC) phases widely exist in the phase diagrams of iron pnictides and chalcogenides. Nevertheless, the origin of the two-dome magnetic and SC phases in iron-based compounds remains unclear. Here we theoretically investigated the electronic structures, magnetic and SC properties of three representative iron-based systems, i.e. LaFeAsO$_{1-x}$H$_{x}$, LaFeAs$_{1-x}$P$_{x}$O and KFe$_{2}$As$_{2}$. We propose a unified quasi-degenerate orbital mechanism for the emergence of the two-dome parent magnetic/structural phase and the subsequent two-dome SC phase. It is found that the degenerate in-plane anisotropic $d_{xz/yz}$ orbitals dominate the first magnetic/structural and SC phases, while in-plane isotropic orbitals $d_{xy}$ or $d_{3z^{2}-r^{2}}$ with quasi-degeneracy originating from quasi-symmetry drive the emergence of the second magnetic/SC dome phase. Moreover, a matching rule of spin and orbital modes for SC pairing state is proposed in multi-orbital iron-based systems. These results imply an orbital-driven mechanism as well as an orbital-selective scenario, and shed light on the understanding of the multi-dome magnetic and SC phases in multi-orbital systems.