Anion height as a controlling parameter for the superconductivity in iron pnictides and cuprates

Both families of high $T_c$ superconductors, iron pnictides and cuprates, exhibit material dependence of superconductivity. Here, we study its origin within the spin fluctuation pairing theory based on multiorbital models that take into account realistic band structures. For pnictides, we show that the presence and absence of Fermi surface pockets is sensitive to the pnictogen height measured from the iron plane due to the multiorbital nature of the system, which is reflected to the nodeless/nodal form of the superconducting gap and $T_c$. Surprisingly, even for the cuprates, which is conventionally modeled by a single orbital model, the multiorbital band structure is shown to play a crucial role in the material dependence of superconductivity. In fact, by adopting a two orbital model that considers the $d_{z^2}$ orbital on top of the $d_{x^2-y^2}$ orbital, we can resolve a long standing puzzle of why the single layered Hg cuprate have much higher $T_c$ than the La cuprate. Interestingly, here again the apical oxygen height measured from the CuO$_2$ plane plays an important role in determining the relative energy difference between $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, thereby strongly affecting the superconductivity.