In bulk materials superconductivity is remarkably robust with respect to nonmagnetic disorder [1]. In the two-dimensional limit however, the quantum condensate suffers from the effects produced by disorder and electron correlations which both tend to destroy superconductivity [2][3][4][5][6][7]. The recent discovery of superconductivity in single atomic layers of Pb, the striped incommensurate (SIC) and √ 7 × √ 3 Pb/Si(111) [8,9], opened an unique opportunity to probe the influence of well-identified structural disorder on two-dimensional superconductivity at the atomic and mesoscopic scale [10,11]. In these two ultimate condensates we reveal how the superconducting spectra loose their conventional character, by mapping the local tunneling density of states. We report variations of the spectral properties even at scales significantly shorter than the coherence length. Furthermore, fine structural differences between the two monolayers, such as their atomic density, lead to very different superconducting behaviour. The denser SIC remains globally robust to disorder, as are thicker Pb films [12-17], whereas in the slighly more diluted √ 7 × √ 3 system superconductivity is strongly fragilized. A consequence of this weakness is revealed at monoatomic steps of √ 7 × √ 3, which disrupt superconductivity at the atomic scale. This effect witnesses that each individual step edge is a Josephson barrier. At a mesoscopic scale the weakly linked superconducting atomic terraces of √ 7 × √ 3 form a native network of Josephson junctions. We anticipate the Pb/Si(111) system to offer the unique opportunity to tune the superconducting coupling between adjacent terraces [18], paving a new way of designing atomic scale quantum devices compatible with silicon technology.

In a direct scanning tunneling spectroscopy experiment we address the problem of the quantum vortex phases in strongly confined superconductors. The strong confinement regime is achieved in in situ grown ultrathin single nanocrystals of Pb by tuning their lateral size to a few coherence lengths. Upon an external magnetic field, the scanning tunneling spectroscopy revealed novel ultradense arrangements of single Abrikosov vortices characterized by an intervortex distance up to 3 times shorter than the bulk critical one. At yet stronger confinement we discovered the giant vortex phase; the spatial evolution of the excitation tunneling spectra in the cores of these unusual quantum objects was explored. We anticipate the giant vortex phase to be a common feature of other confined quantum condensates such as superfluids, Bose-Einstein condensates of cold atoms, etc.