  The interplay between disorder and superconductivity has intrigued physicists
for decades. Of particular interest is the influence of disorder on the
superconducting energy gap $\Delta$. In the absence of Coulomb interactions
between electrons, disorder leads to emergent granularity of the local order
parameter resulting in a pseudogap at temperatures above the critical
temperature $T_c$, as well as a finite gap $\Delta$ on the insulating side of
the disorder-driven superconductor-insulator transition (SIT). At the same
time, disorder also enhances the Coulomb interactions, which subsequently may
influence $\Delta$ in a manner that is still not fully understood. Here we
investigate the evolution of the energy gap through the SIT by two different
experimental methods: tunneling spectroscopy, in which a metallic electrode is
placed close to the studied sample thus screening the Coulomb interactions, and
terahertz (THz) spectroscopy, which probes the unscreened sample. The
comparison between the two methods illustrates the role played by electronic
interactions in determining the nature of the phases across the SIT and sheds
light on the mechanisms involved in the destruction of superconductivity.
