  The interplay of nontrivial topology and superconductivity in condensed
matter physics gives rise to exotic phenomena. However, materials are extremely
rare where it is possible to explore the full details of the superconducting
pairing. Here, we investigate the momentum dependence of the superconducting
gap distribution in a novel Dirac material PdTe. Using high resolution, low
temperature photoemission spectroscopy, we establish it as a spin-orbit coupled
Dirac semimetal with the topological Fermi arc crossing the Fermi level on the
(010) surface. This spin-textured surface state exhibits a fully gapped
superconducting Cooper pairing structure below Tc~4.5K. Moreover, we find a
node in the bulk near the Brillouin zone boundary, away from the topological
Fermi arc.These observations not only demonstrate the band resolved electronic
correlation between topological Fermi arc states and the way it induces Cooper
pairing in PdTe, but also provide a rare case where surface and bulk states
host a coexistence of nodeless and nodal gap structures enforced by spin-orbit
coupling.
