Effect of realistic finite-size impurities on Tc in Fe-based superconductors

Recently, the phase diagram of LaFeAsO$_{1-x}$H$_x$ is reported and two-dome structure of superconducting state, first dome for $x<0.2$ with $T_c^{\rm max}=29$K and second dome for $0.2< x<0.5$ with $T_c^{\rm max}=36$K, has attract great attention[1]. To clarify the origin of the second superconducting dome, we construct tight-binding models for each doping level $x$ and investigate the spin and orbital fluctuations based on the random phase approximation. We fined that the nesting between electron-hole Fermi surfaces is monotonically weakened with $x$ and spin density wave order with momentum ${\bf q}=(\pi,\pi)$ disappears. In the over-doped regime for $x>0.2$, however, the nesting between electron-electron Fermi surfaces increases, and an incommensurate spin density wave order emerges. The orbital order also shows a re-entrant phase diagram. The spin and orbital fluctuations due to the incommensurate nesting would then be the origin of the second superconducting dome reported in the H-over-doped LaFeAsO. The obtained electronic states for $x=0.5$ are very similar to that for KFe$_2$Se$_2$[2], which is a heavily electron doped system(0.5 electron/Fe). [1] S. Iimura, {\it et al.}, Nat. Commumn. {\bf 3}, 943 (2012). [2] T. Saito, {\it et al.}, Phys. Rev. B {\bf 83}, 140512 (2011).