  The search for topological superconductors (TSCs) is one of the most urgent
contemporary problems in condensed matter systems. TSCs are characterized by a
full superconducting gap in the bulk and topologically protected gapless
surface (or edge) states. Within each vortex core of TSCs, there exist the zero
energy Majorana bound states, which are predicted to exhibit non-Abelian
statistics and to form the basis of the fault-tolerant quantum computation. So
far, no stoichiometric bulk material exhibits the required topological surface
states (TSSs) at Fermi level combined with fully gapped bulk superconductivity.
Here, we report atomic scale visualization of the TSSs of the
non-centrosymmetric fully-gapped superconductor, PbTaSe2. Using quasiparticle
scattering interference (QPI) imaging, we find two TSSs with a Dirac point at
E~1.0eV, of which the inner TSS and partial outer TSS cross Fermi level, on the
Pb-terminated surface of this fully gapped superconductor. This discovery
reveals PbTaSe2 as a promising candidate as a TSC.
