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The critical effect of disorder on the two-dimensional (2D) surfacesuperconductor Si(111)-($\sqrt{7}\times\sqrt{3}$)-In is clarified by comparingtwo regions with different degrees of disorder. Low-temperature scanningtunneling microscopy measurements reveal that superconductivity is retained inthe less disordered region, judging from the characteristic differentialconductance ($dI/dV$) spectra and from the formation of vortices under magneticfields. In striking contrast, the absence of those features in the highlydisordered region shows that superconductivity is strongly suppressed there.Analysis of observed zero-bias anomalies in $dI/dV$ spectra allows us toestimate the reduction in the transition temperature $T_{\rm c}$, whichexplains the fate of superconductivity in each region.

Disorder-induced suppression of superconductivity in the Si(111)-($\sqrt{7}\times\sqrt{3}$)-In surface: Scanning tunneling microscopy study