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A bulk superconductor possessing a topological surface state at the Fermilevel is a promising system to realize long-sought topologicalsuperconductivity. Although several candidate materials have been proposed,experimental demonstrations concurrently exploring spin textures andsuperconductivity at the surface have remained elusive. Here we performspectroscopic-imaging scanning tunnelling microscopy on the centrosymmetricsuperconductor $\beta$-PdBi$_2$ that hosts a topological surface state. Bycombining first-principles electronic-structure calculations and quasiparticleinterference experiments, we determine the spin textures at the surface, andshow not only the topological surface state but also all other surface bandsexhibit spin polarizations parallel to the surface. We find that thesuperconducting gap fully opens in all the spin-polarized surface states. Thisbehaviour is consistent with a possible spin-triplet order parameter expectedfor such in-plane spin textures, but the observed superconducting gap amplitudeis comparable to that of the bulk, suggesting that the spin-singlet componentis predominant in $\beta$-PdBi$_2$.

Full-gap superconductivity in spin-polarized surface states of topological semimetal $\beta$-PdBi$_2$