Absence of the Vortex Solution in Gor'kov's Formalism

TL;DR

This paper demonstrates that the Abrikosov vortex solution does not satisfy Gor'kov's formalism's self-consistency equation, indicating limitations in the formalism's ability to describe vortex phenomena in superconductors.

Contribution

It reveals that Gor'kov's formalism cannot produce the Abrikosov vortex solution due to its handling of off-diagonal long-range order.

Findings

Abrikosov vortex solution is not a solution in Gor'kov's formalism

Self-consistency equation involves superposition of different ODLRO types

Potential resolution to the vortex problem is proposed

Abstract

It is shown that the Abrikosov's vortex solution or its corresponding two-particle pair potential is not the solution of the self-consistency equation in Gor'kov's formalism. Since the self-consistency equation leads to a superposition of different types of off-diagonal long-range order (ODLRO) instead of one type of ODLRO only, it may not handle the vortex problem appropriately. A possible resolution is suggested.