A Constraint on the Anomalous Green's Function

TL;DR

This paper demonstrates that the physical constraints on the Anomalous Green's function lead to a natural pairing condition, connecting it to the BCS gap equation and revealing weak localization effects in phonon-mediated interactions.

Contribution

It introduces a fundamental constraint on the Anomalous Green's function that naturally derives the pairing condition and links to the BCS theory, including localization corrections.

Findings

Derivation of a natural pairing condition from Green's function constraints

Connection between the self-consistency equation and the BCS gap equation

Identification of weak localization correction to phonon-mediated interactions

Abstract

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.