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 $T\to 0$. We evaluate the subgap conductance of NS hybrids in the presence of electron-electron interactions and demonstrate that this new length $L_{\phi }$ can be directly extracted from conductance measurements in such structures.