Is electromagnetic gauge invariance spontaneously violated in superconductors?
Abstract
We aim to give a pedagogical introduction to those elementary aspects of superconductivity which are not treated in the classic textbooks. In particular, we emphasize that global U (1) phase rotation symmetry, and not gauge symmetry, is spontaneously violated, and show that the BCS wave function is, contrary to claims in the literature, fully gauge invariant. We discuss the nature of the order parameter, the physical origin of the many degenerate states, and the relation between formulations of superconductivity with fixed particle numbers vs. welldefined phases. We motivate and to some extend derive the effective field theory at low temperatures, explore symmetries and conservation laws, and justify the classical nature of the theory. Most importantly, we show that the entire phenomenology of superconductivity essentially follows from the single assumption of a charged order parameter field. This phenomenology includes Anderson's characteristic equations of superfluidity, electric and magnetic screening, the Bernoulli Hall effect, the balance of the Lorentz force, as well as the quantum effects, in which Planck's constant manifests itself through the compactness of the U (1) phase field. The latter effects include flux quantization, phase slippage, and the Josephson effect.
 Publication:

Annals of Physics
 Pub Date:
 September 2005
 DOI:
 10.1016/j.aop.2005.03.008
 arXiv:
 arXiv:condmat/0503400
 Bibcode:
 2005AnPhy.319..217G
 Keywords:

 74.20.z;
 11.15.q;
 11.15.Ex;
 Theories and models of superconducting state;
 Gauge field theories;
 Spontaneous breaking of gauge symmetries;
 Condensed Matter  Superconductivity
 EPrint:
 18 pages, 2 figures, revtex4