  A theory has been developed to explain the anomalous behavior of the magnetic
susceptibility of a normal metal-superconductor ($NS$) structure in weak
magnetic fields at millikelvin temperatures. The effect was discovered
experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting
samples covered with a thin normal pure metal layer, the susceptibility
exhibited a reentrant effect: it started to increase unexpectedly when the
temperature lowered below 100 mK. The effect was observed in mesoscopic $NS$
structures when the $N$ and $S$ metals were in good electric contact. The
theory proposed is essentially based on the properties of the Andreev levels in
the normal metal. When the magnetic field (or temperature) changes, each of the
Andreev levels coincides from time to time with the chemical potential of the
metal. As a result, the state of the $NS$ structure experiences strong
degeneracy, and the quasiparticle density of states exhibits resonance spikes.
This generates a large paramagnetic contribution to the susceptibility, which
adds up to the diamagnetic contribution thus leading to the reentrant effect.
The explanation proposed was obtained within the model of free electrons. The
theory provides a good description for experimental results [10].

Superconductivity