Experimental evidence of anomalously large superconducting gap on topological surface state of $\beta$-$\mathbf{B}{\mathbf{i}}_{\mathbf{2}}\mathbf{P}\mathbf{d}$ film

Connate topological superconductor (TSC) combines topological surface states with nodeless superconductivity in a single material, achieving effective $p$-wave pairing without interface complication. By combining angle-resolved photoemission spectroscopy and $in$-$situ$ molecular beam epitaxy, we studied the momentum-resolved superconductivity in $\beta$-$\mathrm{B}{\mathrm{i}}_2\mathrm{P}\mathrm{d}$ film. We found that the superconducting gap of topological surface state (${\mathrm{\Delta }}_{TSS}\sim$ 3.8 meV) is anomalously enhanced from its bulk value (${\mathrm{\Delta }}_b\sim$ 0.8 meV). The ratio of $2{\mathrm{\Delta }}_{TSS}\mathrm{/}{k}_B{T}_c\sim 14.2$, is substantially larger than the BCS value. By measuring $\beta$-$\mathrm{B}{\mathrm{i}}_2\mathrm{P}\mathrm{d}$ bulk single crystal as a comparison, we clearly observed the upward-shift of chemical potential in the film. In addition, a concomitant increasing of surface weight on the topological surface state was revealed by our first principle calculation, suggesting that the Dirac-fermion-mediated parity mixing may cause this anomalous superconducting enhancement. Our results establish $\beta$-$\mathrm{B}{\mathrm{i}}_2\mathrm{P}\mathrm{d}$ film as a unique case of connate TSCs with a highly enhanced topological superconducting gap, which may stabilize Majorana zero modes at a higher temperature.