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A well-known result in unconventional superconductivity is the fragility ofnodal superconductors against nonmagnetic impurities. Despite this commonwisdom, Bi$_2$Se$_3$-based topological superconductors have recently displayedunusual robustness against disorder. Here we provide a theoretical frameworkwhich naturally explains what protects Cooper pairs from strong scattering incomplex superconductors. Our analysis is based on the concept ofsuperconducting fitness and generalizes the famous Anderson's theorem intosuperconductors having multiple internal degrees of freedom. For concreteness,we report on the extreme example of the Cu$_x$(PbSe)$_5$(Bi$_2$Se$_3$)$_6$superconductor, where thermal conductivity measurements down to 50 mK not onlygive unambiguous evidence for the existence of nodes, but also reveal that theenergy scale corresponding to the scattering rate is orders of magnitude largerthan the superconducting energy gap. This provides a most spectacular case ofthe generalized Anderson's theorem protecting a nodal superconductor.

Generalized Anderson's theorem for superconductors derived from topological insulators