Reinvestigation of Inhomogeneous Superconductors and High $T_{c}$ Superconductors

TL;DR

This paper reviews recent theoretical advances in understanding inhomogeneous and high-temperature superconductors, emphasizing the need for pairing constraints in Green's function and Bogoliubov-de Gennes formalisms, and discusses implications for impurity effects and inhomogeneous systems.

Contribution

It introduces a revised theoretical framework with pairing constraints for inhomogeneous superconductors, prompting a reinvestigation of their properties and impurity effects.

Findings

Revised pairing constraints improve the accuracy of superconductor models.

Impurity doping effects in high $T_c$ superconductors are better understood.

New formalism needed for inhomogeneous systems like junctions and vortices.

Abstract

We review the recent progress in the theory of inhomogeneous superconductors. It was shown that Gor'kov's self-consistency equation needs a pairing constraint derived from the Anomalous Green's function. The Bogoliubov-de Gennes equations also need a pairing constraint in order to obtain a correct vacuum state by the corresponding unitary transformation. This new study opens up a reinvestigation of inhomogeneous superconductors. We discuss (i) problems of the conventional Green's function theory, (ii) reinvestigation of impure superconductors, and (iii) impurity doping effect in high $T_{c}$ superconductors. It is also pointed out that a new formalism is required to tackle the macroscopically or mesoscopically inhomogeneous systems such as the junction and the vortex problems.