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Superconducting proximity effects in metals with a repulsive pairing interaction

Studies of the superconducting proximity effect in normal conductor/superconductor $(N/S)$ junctions almost universally assume no effective electron-electron coupling in the $N$ region. While such an approximation leads to a simple description of the proximity effect, it is unclear how it could be rigorously justified. We reveal a much more complex picture of the proximity effect in $N/S$ bilayers, where $S$ is a clean s-wave BCS superconductor and $N$ is a simple metal with a repulsive effective electron coupling. We elucidate the proximity effect behavior using a highly accurate method to self-consistently solve the Bogoliubov-deGennes equations. We present our results for a wide range of values of the interface scattering, the Fermi wave vector mismatch, the temperature, and the ratio $g$ of the effective interaction strengths in the $N$ and $S$ region. We find that the repulsive interaction, represented by a negative $g$, strongly alters the signatures of the proximity effect as can be seen in the spatial dependence of the Cooper pair amplitude and the pair potential, as well as in the local density of states near the interface.