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Recently discovered (CaFe$_{1-x}$Pt$_x$As)$_{10}$Pt$_3$As$_8$ and(CaFeAs)$_{10}$Pt$_{4-y}$As$_8$ superconductors are very similar materialshaving the same elemental composition and structurally similar superconductingFeAs slabs. Yet the maximal critical temperature achieved by changing Ptconcentration is approximately twice higher in the latter. Using angle-resolvedphotoemission spectroscopy(ARPES) we compare the electronic structure of theiroptimally doped compounds and find drastic differences. Our results highlightthe sensitivity of critical temperature to the details of fermiology and pointto the decisive role of band-edge singularities in the mechanism of high-$T_c$superconductivity.

Why $T_c$ of (CaFeAs)$_{10}$Pt$_{3.58}$As$_8$ is twice as high as (CaFe$_{0.95}$Pt$_{0.05}$As)$_{10}$Pt$_3$As$_8$