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Maximizing Fermi surface multiplicity optimizes superconductivity in iron pnictides

We study the condition for optimizing superconductivity in the iron pnictides from the lattice structure point of view. Studying the band structure of the hypothetical lattice structure of LaFeAsO, the hole Fermi surface multiplicity is found to be maximized around the Fe-As-Fe bond angle regime where the arsenic atoms form a regular tetrahedron. Superconductivity is optimized within this three hole Fermi surface regime, while the stoner factor of the antiferromagnetism has an overall tendency of increasing upon decreasing the bond angle. Combining also the effect of the varying the Fe-As bond length, we provide a guiding principle for obtaining high $T_c$.