Parity Effect in SN-Proximity-Systems

•Harald Kloos und Andrei Zaikin
Forschungszentrum Karlsruhe, Institut für Nanotechnologie, 76021 Karlsruhe, Germany

A normal metal layer in good electric contact to a superconductor exhibits properties sumarized under the term proximity effect, i.e. Andreev reflection and the formation of a gap in the density of states which is much smaller than the superconducting order parameter D. At low temperatures thermodynamic properties of small isolated superconducting grains depend on the parity of the number of electrons they carry, because pairs of electrons can form Cooper pairs and enter the condensate, whereas the lowest available state for an unpaired electron is given by D. We investigate the parity effect in an SN layer structure within the quasiclassical Green's functions formalism for arbitrary concentrations of nonmagnetic impurities. The temperature T* is estimated, below which parity effects dominate the physical properties of the sample due to the proximity induced features of the N-layer. It is shown that the free energy difference between ensembles with even and odd numbers of particles at zero temperature coincides with the proximity gap of the normal metal layer. At finite temperatures the entropy factor is related to the density of states of the sample.