The conductance of superconducting-normal hybrid structures

The dc conductance of normal-superconducting hybrid structures is discussed, in connection with
the superconducting-insulating transition. Emphasizing the role of the Andreev reections at the
superconducting-normal metal interface, 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 composite to become insulating. We also show that since
the Bogoliubov-DeGennes equation does not conserve charge, its application to create a Landauer-
type approach for the conductance of the hybrid system is problematic. We `mend' this deficiency
by calculating the conductance from the Kubo formula for a special configuration.