Relationship between structure anisotropy and T$_{\mathrm{C}}$ and phase diagram of AFe$_{\mathrm{2}}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{2}$ (A$=$Ba, Sr, Ca)

We investigated how the electronic phase diagram changes when the crystal structure changes in $A$Fe$_{2}$(As$_{\mathrm{1-y}}$P$_{\mathrm{y}})_{2}$ where $A=$Ba/Sr or Sr/Ca. In this study, we synthesized the single crystals of Ba$_{0.5}$Sr$_{0.5}$Fe$_{2}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{2}$, Sr$_{0.92}$Ca$_{0.08}$Fe$_{2}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{2}$ and Sr$_{0.84}$Ca$_{0.16}$Fe$_{2}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{2}$, measured the resistivity and determined precise structure parameters using synchrotron X-ray, then elucidated their phase diagrams and detailed crystal structures. The phase diagram of $A=$Ba$_{0.5}$Sr$_{0.5}$ system is similar to those for $A=$Ba and Sr, while for $A=$Sr/Ca systems the superconducting phase appears at a smaller P content than the case for $A=$Ba and Sr. The important finding is that the maximum $T_{\mathrm{C}}$ values are almost the same in all $A$Fe$_{2}$(As$_{\mathrm{1-y}}$P$_{\mathrm{y}})_{2} $systems. From the X-ray structural analysis, it has been revealed that in the optimally doped crystals, the local structures of FeAs$_{4}$ tetrahedra such as pnictogen heights or bond angles of As-Fe-As are almost the same, whereas the anisotropy of the crystal structures,$ c$/$a$, systematically changes. We conclude that $T_{\mathrm{C}}$ is not affected by the anisotropy ($c$/$a)$ but strongly depends on the local structure such as the pnictogen height.