Orbital Paramagnetism of Electrons in Proximity to a Superconductor

We consider the magnetic response of a normal layer ( $N$) coating a superconducting cylinder ( $S$). The diamagnetic response of the normal layer (proximity effect) is related to the formation of Andreev levels. At low energies, the density of such states goes linearly to zero which enhances the various scattering mean-free paths. As a consequence, the low-energy glancing states, which can skip along the outer boundary, can have relatively large magnetic moments that lead to a low-temperature paramagnetic correction to the Meissner result.