Conductance of superconducting-normal hybrid structures

The dc conductance of normal-superconducting hybrid structures is discussed. It is shown that since the Bogoliubov-DeGennes (BDG) equation does not conserve charge, its application to create a Landauer-type approach for the conductance of the NSN system is problematic. We "mend" this deficiency by calculating the conductance from the Kubo formula for a ring configuration, where charge conservation is imposed by the annular geometry. We show that the presence of a superconductor segment within an otherwise normal metal may reduce the overall conductance of the composite structure. This reduction enhances the tendency of the NS composite to become insulating.