The 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 (for this geometry the solutions of the BDG equation conserve charge). We show that the presence of a superconductor segment within an otherwise normal metal may {\em reduce} the overall conductance of the composite structure. This reduction enhances the tendency of the NS composite to become insulating.