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Origin of the non-monotonic variance of Tc in the 1111 iron based superconductors with isovalent doping

Motivated by recent experimental investigations of the isovalent doping iron-based superconductors LaFe(AsxP1-x)O1-yFy and NdFe(AsxP1-x)O1-yFy we theoretically study the correlation between the local lattice structure, the Fermi surface, the spin fluctuation-mediated superconductivity, and the composition ratio. In the phosphides, the dXZ and dYZ orbitals barely hybridize around the Gamma point to give rise to two intersecting ellipse shape Fermi surfaces. As the arsenic content increases and the Fe-As-Fe bond angle is reduced, the hybridization increases, so that the two bands are mixed to result in concentric inner and outer Fermi surfaces, and the orbital character gradually changes to dxz and dyz, where x-y axes are rotated by 45 degrees from X-Y. This makes the orbital matching between the electron and hole Fermi surfaces better and enhances the spin fluctuation within the dxz/yz orbitals. On the other hand, the hybridization splits the two bands, resulting in a more dispersive inner band. Hence, there is a trade-off between the density of states and the orbital matching, thereby locally maximizing the dxz/yz spin fluctuation and superconductivity in the intermediate regime of As/P ratio. The consistency with the experiment strongly indicate the importance of the spin fluctuation played in this series of superconductors.