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Pnictogen height as a possible switch between high-T_c nodeless and low-T_c nodal pairings in the iron based superconductors

We study the effect of the lattice structure on the spin-fluctuation mediated superconductivity in the iron pnictides adopting the five-band models of several virtual lattice structures of LaFeAsO as well as actual materials such as NdFeAsO and LaFePO obtained from the maximally-localized Wannier orbitals. Random phase approximation is applied to the models to solve the Eliashberg equation. This reveals that the gap function and the strength of the superconducting instability are determined by the cooperation or competition among multiple spin fluctuation modes arising from several nestings among disconnected pieces of the Fermi surface, which is affected by the lattice structure. Specifically, the appearance of the Fermi surface $γ$ around $(π,π)$ in the unfolded Brillouin zone is sensitive to the pnictogen height $h_{\rm Pn}$ measured from the Fe plane, where $h_{\rm Pn}$ is shown to act as a switch between high-$T_c$ nodeless and low-$T_c$ nodal pairings. We also find that reduction of the lattice constants generally suppresses superconductivity. We can then combine these to obtain a generic superconducting phase diagram against the pnictogen height and lattice constant. This suggests that NdFeAsO is expected to exhibit a fully-gapped, sign-reversing s-wave superconductivity with a higher $T_c$ than in LaFeAsO, while a nodal pairing with a low $T_c$ is expected for LaFePO, which is consistent with experiments.