B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine
Received May 17, 2016, revised August 1, 2016
It is shown that in equilibrium superconducting structures with s-wave-type pairing the single-valued part of the complex order parameter (quasi-average) 〈ψ↑ψ↓〉 is transformed into the longitudinal component of the vector potential as in the Abelian Higgs model of the relativistic field theory. The consideration is based on the microscopic Hamiltonian of the system in the presence of an external static magnetic field and infinitesimally small sources of Cooper pairs. The presence of impurities and non-superconducting barriers is envisaged and quantum nature of the induced electromagnetic field is also taken into account. The quantization of the latter is carried out under the condition A0 = 0 (with A0 being the scalar potential), which does not violate invariance with respect to gauge transformations that do not depend on time. Ex-act relations determining the quasi-average 〈ψ↑ψ↓〉 are established. These relations play a key role in a new derivation of the mean-field equations that is presented in the paper. On the basis of the obtained results, a new physical interpretation of the Josephson effect (without “phase differences») is proposed and some consequences are discussed.
PACS: 74.20.Fg BCS theory and its development; PACS: 11.15.Ex Spontaneous breaking of gauge symmetries; PACS: 74.50.+r Tunneling phenomena; Josephson effects.