  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.
