Direct evidence for Cooper pairing without a spectral gap in a disordered superconductor above $T_{C}$

The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron charges. We further show that spectroscopic gap fills up rather than closes when increasing temperature. Our results thus demonstrate the existence of a novel state above $T_{C}$ that, much like an ordinary metal, has no (pseudo)gap, but carries charge via paired electrons.