Superconductivity near the saddle point in the two-dimensional Rashba system Si(111)−3×3−(Tl,Pb)

Two-dimensional Rashba superconductor\nSi(111)-$\\sqrt{3}\\times\\sqrt{3}$-(Tl,Pb) is a candidate platform of mixed\nspin-singlet and -triplet superconductivity. A recent scanning tunneling\nmicroscope (STM) experiment revealed a pseudogap at the vortex core, suggesting\nthe finite triplet component [T. Nakamura $\\textit{et al.}$, Phys. Rev. B $\\bf{\n98}$, 134505 (2018)]. Detailed spectroscopic information of the superconducting\ngap and the low-energy band structure is necessary to establish the putative\ntriplet superconductivity. Here, we performed high-energy-resolution\nspectroscopic imaging experiments on Si(111)-$\\sqrt{3}\\times\\sqrt{3}$-(Tl,Pb)\nusing an ultra-low temperature STM. We found that various spectroscopic\nfeatures, including the vortex-core spectrum, are consistent with spin-singlet\n$s$-wave superconductivity, having no sign of the triplet component. The\napparent contradiction with the previous STM result suggests that the nature of\nsuperconductivity changes within the same system. From the analysis of the\nquasiparticle interference patterns, we found that the Fermi energy is in the\nclose vicinity of the saddle point near the $\\overline{\\rm{M}}$ point. We\nspeculate that the nature of superconductivity varies depending on the\nsaddle-point energy with respect to the Fermi energy, which is sample-dependent\ndue to different band filling.\n