  The most profound effect of disorder on electronic systems is the
localization of the electrons transforming an otherwise metallic system into an
insulator. If the metal is also a superconductor then, at low temperatures,
disorder can induce a dramatic transition from a superconducting into an
insulating state. An outstanding question is whether the route to insulating
behavior proceeds via the direct localization of Cooper pairs or,
alternatively, by a two-step process in which the Cooper pairing is first
destroyed followed by the standard localization of single electrons. Here we
address this question by studying the local superconducting gap of a highly
disordered, amorphous, superconductor by means of scanning tunneling
spectroscopy. Our measurements reveal that, in the vicinity of the
superconductor-insulator transition, the coherence peaks in the one-particle
density of states disappear while the superconducting gap remains intact
indicating the presence of localized Cooper pairs. Our results provide the
first direct evidence that the transition in our system is driven by Cooper
pair localization.
