Dependence of carrier doping on the impurity potential in transition-metal-substituted FeAs-based superconductors

In order to examine to what extent the rigid-band-like electron doping scenario is applicable to the transition metal-substituted Fe-based superconductors, we have performed angle-resolved photoemission spectroscopy studies of Ba(Fe$_{1-x}$Ni$_{x}$)$_2$As$_2$ (Ni-122) and Ba(Fe$_{1-x}$Cu$_{x}$)$_2$As$_2$ (Cu-122), and compared the results with Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ (Co-122). We find that Ni 3$\it{d}$-derived features are formed below the Fe 3$\it{d}$ band and that Cu 3$\it{d}$-derived ones further below it. The electron and hole Fermi surface (FS) volumes are found to increase and decrease with substitution, respectively, qualitatively consistent with the rigid-band model. However, the total extra electron number estimated from the FS volumes (the total electron FS volume minus the total hole FS volume) is found to decrease in going from Co-, Ni-, to Cu-122 for a fixed nominal extra electron number, that is, the number of electrons that participate in the formation of FS decreases with increasing impurity potential. We find that the N$\acute{\rm{e}}$el temperature $T_{\rm{N}}$ and the critical temperature $T_{\it{c}}$ maximum are determined by the FS volumes rather than the nominal extra electron concentration nor the substituted atom concentration.