Meissner effect in gauge-invariant, self-consistent pairing theories

Abstract

Within the frame of a self-consistent pairing theory, with potential interelectron interaction, a gauge-invariant discussion of the Meissner effect is given. It is shown that the terms that are usually ignored, proportional to the variation of the order parameter due to the magnetic field, are indeed vanishing in the Coulomb gauge, provided that the pairing phase is locally stable. An instructive example is given, where due to the degeneracy of the phase, although a pairing gap exists, there is no Meissner effect at all.