On the electrodynamic Londons’ model and the Gorter–Casimir theory

Abstract

The classical phenomenological Londons’ theory of superconductivity is analyzed in detail. The incorrectness of the derivation of the basic system of equations and the lack of evidentiary support of the assumption concerning the irrotational fluid flow of superconducting electrons are shown. It is concluded that, for superconductors, it is impossible to determine the vector of the magnetic-field strength unambiguously, since it is unclear how to divide the superconducting current into the conduction current and the magnetizing current. The concentration of electrons is refined within the framework of the Gorter–Casimir model of a two-component electron fluid in superconductors with the Drude–Lorentz–Sommerfeld theory taken into account. The temperature dependence of the critical magnetic field is calculated and compared with the classical result. It is shown that this parameter can be changed within a rather wide range within the framework of accuracy of the experimental data. Based on results obtained for constant currents in materials with a high conductivity, a hypothesis about identification of the thickness of the thin layer in which surface currents flow with a depth of penetration of the magnetic field into the material is proposed.