Vortex lattices and the Bogoliubov-de Gennes equations

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

The passage discusses the use of Bogoliubov-de Gennes equations to provide an equivalent formulation of the BCS theory of superconductivity, focusing on static solutions with a magnetic field present. It carefully formulates the equations in a basis independent form, discusses their general features, and isolates key physical classes of solutions (normal and vortex lattice states) which are candidates for the ground state. It proves the existence of normal and vortex lattice states and their stability in certain temperature and magnetic field ranges.