  The notion of spontaneous formation of an inhomogeneous superconducting state
is at the heart of most theories attempting to understand the superconducting
state in the presence of strong disorder. Using scanning tunneling spectroscopy
and high resolution scanning transmission electron microscopy, we
experimentally demonstrate that under the competing effects of strong
homogeneous disorder and superconducting correlations, the superconducting
state of a conventional superconductor, NbN, spontaneously segregates into
domains. Tracking these domains as a function of temperature we observe that
the superconducting domains persist across the bulk superconducting transition,
Tc, and disappear close to the pseudogap temperature, T*, where signatures of
superconducting correlations disappear from the tunneling spectrum and the
superfluid response of the system.
