  Surfaces of three-dimensional topological insulators have emerged as one of
the most remarkable states of condensed quantum matter1-5 where exotic
electronic phases of Dirac particles should arise1,6-8. Here we report a
discovery of surface superconductivity in a topological material (Sb2Te3) with
resistive transition at a temperature of ~9 K induced through a minor tuning of
growth chemistry that depletes bulk conduction channels. The depletion shifts
Fermi energy towards the Dirac point as witnessed by about two orders of
magnitude reduction of carrier density and by very large (~25,000 cm^2/Vs)
carrier mobility. Direct evidence from scanning tunneling spectroscopy and from
magnetic response show that the superconducting condensate forms in surface
puddles at unprecedentedly higher temperatures, near 60 K and above. The new
superconducting state we observe to emerge in puddles can be tuned by the
topological material's parameters such as Fermi velocity and mean free path
through band engineering; it could potentially become a hunting ground for
Majorana modes6 and lead to a disruptive paradigm change9 in how quantum
information is processed.
