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Dephasing of Cooper pairs and subgap electron transport in superconducting hybrids

We argue that electron-electron interactions fundamentally restrict the penetration length of Cooper pairs into a diffusive normal metal (N) from a superconductor (S). At low temperatures this Cooper pair dephasing length $L_φ$ remains finite and does not diverge at $T \to 0$. We evaluate the subgap conductance of NS hybrids in the presence of electron-electron interactions and demonstrate that this new length $L_φ$ can be directly extracted from conductance measurements in such structures.