  In bulk materials superconductivity is remarkably robust with respect to
non-magnetic disorder. 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 . The recent
discovery of superconductivity in single atomic layers of Pb, the striped
incommensurate (SIC) and $\sqrt{7}\times\sqrt{3}$ Pb/Si(111), opened an unique
opportunity to probe the influence of well-identified structural disorder on
two-dimensional superconductivity at the atomic and mesoscopic scale. 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, whereas in the slighly more diluted
$\sqrt{7}\times\sqrt{3}$ system superconductivity is strongly fragilized. A
consequence of this weakness is revealed at monoatomic steps of
$\sqrt{7}\times\sqrt{3}$, 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
$\sqrt{7}\times\sqrt{3}$ 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, paving a new way of
designing atomic scale quantum devices compatible with silicon technology.
