Vortex Lattices and the Bogoliubov-De Gennes Equations

TL;DR

This paper studies the Bogoliubov-de Gennes equations in superconductivity, proving the existence and stability of normal and vortex lattice states under various temperature and magnetic field conditions.

Contribution

It provides a basis-independent formulation of the equations and establishes the existence and stability properties of key physical solutions.

Findings

Normal states are stable at high temperature or magnetic fields.

Vortex lattice states exist as solutions to the equations.

Normal states become unstable at low temperature and magnetic fields.

Abstract

We consider the Bogoliubov-de Gennes equations giving an equivalent formulation of the BCS theory of superconductivity. We are interested in static solutions with the magnetic field present. We carefully formulate the equations in the basis independent form, discuss their general features and isolate key physical classes of solutions (normal and vortex lattice states) which are the candidates for the ground state. We prove existence of the normal and vortex lattice states and stability of the normal states for large temperature or magnetic fields and their instability for small temperature and small magnetic fields.