  Recently we have described materials interface transport coupling rigorously
utilizing NEGF nonequilibrium Green's functions, and have discussed the
Hamiltonian terms that from Green's theorem and boundary conditions can be
rewritten as Self Energy. We derive the application of our theory to the high
$Tc$ Superconducting materials interfaces that are the composition of the high
temperature superconducting materials. The derivation models a non super-cell
geometry of plaquettes that will describe the superconducting 2D material in
abrupt coupling with the material of insulating or normal conducting
composition.
