On the Bogolubov-de Gennes Equations

TL;DR

This paper analyzes the Bogolubov-de Gennes equations within BCS superconductivity theory, focusing on solutions under magnetic fields, including normal, vortex, and vortex lattice states, and investigates their existence and stability conditions.

Contribution

It provides a comprehensive analysis of the Bogolubov-de Gennes equations with magnetic fields, establishing existence and stability results for various physical states.

Findings

Existence of normal, vortex, and vortex lattice states.

Stability and instability conditions for these states.

Dependence of solutions on temperature and magnetic field strength.

Abstract

We consider the Bogolubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in the case when the magnetic field is present. We (a) discuss their general features, (b) isolate key physical classes of solutions (normal, vortex and vortex lattice states) and (c) prove existence of the normal, vortex and vortex lattice states and stability/instability of the normal states for large/small temperature or/and magnetic fields.