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-phi remains finite and does not diverge at T -> 0. We evaluate the subgap conductance of NS hybrids in the presence of electron-electron interactions and demonstrate that this length L-phi can be directly extracted from conductance measurements in such structures