  Superconductivity on the surface of topological insulators is known to be
anisotropic and unconventional in that the symmetry is the mixture of s-wave
and nodeless p-wave component. In contrast to Anderson's theorem for the
insensitivity of the s-wave superconducting critical temperature to the
nonmagnetic (time-reversal symmetric (TRS)) impurities, anisotropic
superconductors including nodeless p-wave one are in general fragile even with
small concentration of the TRS impurities. By employing the Abrikosov-Gor'kov
theory, we clarify that this type of unconventional superconductivity emergent
on the surface state of the strong topological insulators robustly survive
against TRS impurities.
