Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators

We self-consistently study surface states of superconducting topological insulators. We clarify that, if a topologically trivial bulk s-wave pairing symmetry is realized, parity mixing of pair potential near the surface is anomalously enhanced by surface Dirac fermions, opening an additional surface gap larger than the bulk one. In contrast to classical s-wave superconductors, the resulting surface density of state hosts an extra coherent peak at the induced gap besides a conventional peak at the bulk gap. We also find that no such extra peak appears for odd-parity superconductors with a cylindrical Fermi surface. Our calculation suggests that the simple U-shaped scanning tunneling microscope spectrum in Cu$_x$Bi$_2$Se$_3$ does not originate from s-wave superconductivity, but can be explained by odd-parity superconductivity with a cylindrical Fermi surface.