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The idea that preformed Cooper pairs could exist in a superconductor at temperatures higher than its zero-resistance critical temperature (Tc) has been explored for unconventional, interfacial, and disordered superconductors, but direct experimental evidence is lacking. We used scanning tunneling noise spectroscopy to show that preformed Cooper pairs exist up to temperatures much higher than Tc in the disordered superconductor titanium nitride by observing an enhancement in the shot noise that is equivalent to a change of the effective charge from one to two electron charges. We further show that the spectroscopic gap fills up rather than closes with increasing temperature. Our results demonstrate the existence of a state above Tc that, much like an ordinary metal, has no (pseudo)gap but carries charge through paired electrons. [ABSTRACT FROM AUTHOR]

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of topological quantum chemistry to superconductivity. [ABSTRACT FROM AUTHOR]