Why New Theory?
- There are a few good reasons!
1) There are many fundamental outstanding problems, such as the gauge problem
of the BCS theory and the discrepancies between experiments and the theory.
2) The Gor'kov's formalism and the Bogoliubov-de Gennes equations are not a
proper generalization of the BCS theory.
=> The generalization has been turned out to be the mathematical artifact, due to the violation of the physical constraint of the system. (We may say 2003 Nobel prize appreciated this.)
- Pairing problem in the Gor'kov's formalism [1, 2]
It was believed that choosing a proper form of the pair potential in the Gor'kov's self-consistency equation leads to the correct pairing in the presence of perturbations. However, we showed that the kernel should also be constrained by the ground state, i.e.,
Here P denotes the pairing constraint.
- Pairing problem in the Bogoliubov-de Gennes equations 
By the same token, the Bogoliubov-de Gennes equations need a pairing constraint, derived from the physical constraint
of the system
Here ψn is the normal state eigenfunction