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The family of multi-layered superconductors derived from the dopedtopological insulator Bi$_2$Se$_3$ has been found to be unusually robustagainst non-magnetic disorder. Recent experimental studies have highlighted thefact that the location of impurities could play a critical role for thispuzzling robustness. Here we investigate the effects of four different types ofimpurities, on-site, interstitial, intercalated and polar, on thesuperconducting critical temperature. We find that different components of thescattering potential are active depending on the impurity configuration andchoice of orbitals for the effective low-energy description of the normalstate. For the specific case of Bi$_2$Se$_3$-based superconductors, we findthat only the symmetric share of impurity configurations contribute toscattering, such that polar impurities are completely inactive. We also findthat a more dominant mass-imbalance term in the normal-state Hamiltonian canmake the superconducting state more robust to intercalated impurities, incontrast to the case of on-site or interstitial impurities.

Sensitivity of superconducting states to the impurity location in layered materials