Superconductivity and Magnetism in the Checkerboard Models for Iron-based Superconductors

We study three different checkerboard models for iron-based superconductors and obtain their phase diagrams in the solvable limit of weakly coupled checkerboards. We demonstrate that the strongest superconducting pairing is in the $A_{1g}$-S wave channel and the development of the superconductivity (SC) is correlated with the emergence of the next nearest neighbor antiferromagnetism (AFM). Moreover, this study suggests that the superconductivity and magnetism are orbital-selective. In the three-band model, the AFM is more robust in the $d_{xy}$ orbital and the superconductivity is easier to be generated in the $d_{xz}$ and $d_{yz}$ orbitals. Comparisons between our theoretical results and current experimental measurements are discussed.