Superconducting Topological Surface States in Noncentrosymmetric Bulk Superconductor PbTaSe$_{\mathrm{2}}$

The search for topological superconductors (TSCs) is one of the most exciting problems in condensed matter systems. 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 E$_{\mathrm{F}}$ combined with fully gapped bulk superconductivity. Here, we report atomic scale visualization of the TSSs of the noncentrosymmetric superconductor, PbTaSe2. Our quasiparticle scattering interference imaging shows two TSSs with a Dirac point at E\textasciitilde 1.0eV, of which the inner TSS and partial outer TSS cross E$_{\mathrm{F}}$, on the Pb-surface of this fully gapped superconductor. Our results reveal PbTaSe2 as a promising candidate as a TSC.