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The paper proposes a self-consistent Green function description of theinduced surface superconductivity in a disordered three-dimensional topologicalinsulator (TI) coupled to an s-wave superconductor. We recover earlier resultsregarding the induced spin-triplet p-wave pairing, showing that a mixture of p-and s-wave pair correlations appears as a result of broken spin-rotationsymmetry on the helical surface of the TI. Unlike the s-wave pairing, thep-wave component is found to be suppressed in dirty TIs in which the elasticmean-free path is much smaller than the superconducting coherence length. Thesuppression is due to the generic nonlocality of the spin-triplet correlations,which makes them strongly dependent on the mean-free path in a disorderedsystem. In dirty TIs the induced superconductivity is predicted to bepredominantly s-wave like. In cleaner TIs, however, the p-wave component mayreach a magnitude comparable with (but not larger than) the s-wave pairing.

Suppression of surface p-wave superconductivity in disordered topological insulators