Pairing in the Bogoliubov-de Gennes equations

It is shown that the Bogoliubov-de Gennes equations pair the electrons in states which are linear combinations of the normal states. Accordingly, the BCS-like reduction procedure is required to choose a correct pairing. For a homogeneous system, we point out that the kernel of the self-consistency equation derived from the Bogoliubov-de Gennes equations needs to be constrained by the BCS pairing condition. In the presence of ordinary impurities, on the other hand, the Bogoliubov-de Gennes equations should be supplemented by Anderson's pairing condition to obtain the correct vacuum state by the corresponding unitary transformation. This results in localization correction to the phonon-mediated interaction.Comment: 16 pages, revtex, no figures, to appear in Int. J. Mod. Phys.

Threshold Resistance in the DC Josephson Effect

We show that SIS Josephson junctions have a threshold resistance, above which the Josephson coupling and the supercurrents become extremely small, due to the shrinking of the Cooper pair size during the Josephson tunneling. Accordingly, the threshold resistance is smaller for higher Tc superconductors with small Cooper pair size and for the insulating barrier with higher resistance. This understanding agrees with the observations in SIS junctions of low Tc superconductors, such as Sn, Pb, and Nb. For MgB2 it explains why the big gap does not show the supercurrents, unlike the small gap. Furthermore, it is consistent with the fact that high Tc cuprates show the Josephson effects only for SNS type junctions, including the intrinsic Josephson effects.Comment: Proceedings of LT24 Conference, 2 pages, 1 figure. For more information, please see http://www.superconductivity.us (1 RA position available

A Constraint on the Anomalous Green's Function

It is shown that the physical constraint of the Anomalous Green's function gives a natural pairing condition. The resulting self-consistency equation is directly related to the BCS gap equation. Both inhomogeneous and homogeneous systems are considered to illustrate the importance of the constraint. Especially we find weak localization correction to the phonon-mediated interaction.Comment: 14 pages, latex, no figure