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We demonstrate that electron-electron interactions fundamentally restrict thepenetration length of superconducting correlations into a diffusive normalmetal (N) attached to a superconductor (S). We evaluate the subgapmagnetoconductance $G$ of SN hybrids in the presence of electron-electroninteractions and demonstrate that the effect of the magnetic field on $G$ istwofold: It includes ($i$) additional temperature independent dephasing ofCooper pairs and ($ii$) Zeeman splitting between the states with oppositespins. The dephasing length of Cooper pairs can be directly extracted frommeasurements of the subgap magnetoconductance in SN systems at lowtemperatures.

Decoherence of Cooper pairs and subgap magnetoconductance of superconducting hybrids