Stable vortices in the anomalous metallic state observed on monoatomic-layer superconductors

The superconductor-insulator transition in two-dimensional (2D) systems has been extensively studied as a typical example of quantum phase transition. Recent investigations of highly conductive 2D systems have revealed an intervening metallic regime, in which the electrical resistivity saturates at the limit of zero temperature. The nature and origin of this metallicity remain debated, partly because of the lack of microscopic understanding. In this study, using scanning tunneling spectroscopy, we investigate the metallic state and other phases observed in crystalline Pb monoatomic-layer superconductors formed on vicinal semiconducting substrates. Our spectroscopic images reveal stable and isolated vortices in the metallic regime, distinct from delocalized or liquidized vortices. These findings suggest that the saturated resistance in the metallic state arises from the pinning-free vortex motion driven by the finite current applied for the transport measurements. Our disorder-controlled microscopic experiments provide new insights into the fluctuation-induced phases of ultrathin crystalline 2D superconductors.