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Unfolding the electronic structure of Ca$_{10}$(Fe$_{1-x}$Pt$_x$As)$_{10}$(Pt$_n$As$_8$)

The platinum iron arsenides Ca$_{10}$(Fe$_{1-x}$Pt$_x$As)$_{10}$(Pt$_n$As$_8$) are the first Fe based superconductors with metallic spacer layers. Furthermore they display a large variation in their critical temperatures depending on the amount of Pt in their spacer layers: $(n=3,4)$. To gain more insight into the role of the spacer layer the electronic structures of the iron arsenic platenides are represented in the momentum space of the underlying Fe sublattice using a first principles unfolding method. We find that Ca$_{10}$(FeAs)$_{10}$(Pt$_4$As$_8$), contrary to Ca$_{10}$(FeAs)$_{10}$(Pt$_3$As$_8$), shows a net electron doping and a non-negligible interlayer coupling. Both effects could account for the difference in the critical temperatures.