Role of Sn impurity on electronic topological transitions in 122 Fe-based superconductors

We show that only a few percentage of Sn doping at the Ba site on BaFe$_2$As$_2$, can cause electronic topological transition, namely, the Lifshitz transition. A hole like d$_{xy}$ band of Fe undergoes electron like transition due to 4\% Sn doping. Lifshitz transition is found in BaFe$_2$As$_2$ system around all the high symmetry points. Our detailed first principles simulation predicts absence of any Lifshitz transition in other 122 family compounds like SrFe$_2$As$_2$, CaFe$_2$As$_2$. This work bears practical significance due to the facts that a few percentage of Sn impurity is in-built in tin-flux grown single crystals method of synthesizing 122 materials and inter-relationship among the Lifshitz transition, magnetism and superconductivity.