General expressions for the current density for superconductors in a transverse electromagnetic field are derived from a Green's-function formulation. They are sufficiently general to apply to cases of strong coupling, to superconductors with magnetic impurities, and to anisotropic materials. It is explicitly shown that the response function satisfies ${\lim }_{q\to 0}{\lim }_{\omega \to 0}K(q,\omega )=K(0,0)={\lim }_{\omega \to 0}{\lim }_{q\to 0}K(q,\omega ).\mathrm{}$ The condition for superconductivity is that $K(0,0)\mathrm{}$ be nonvanishing. An expression for the current density in real space in a form similar to that of Mattis and Bardeen is obtained. Various limiting forms of the expressions are derived to facilitate applications to various problems. An expression for the Josephson tunelling current which can be applied to strong-coupling and impure superconductors is derived under the assumption that the tunnelling matrix element is constant.

• Received 28 October 1966

DOI:https://doi.org/10.1103/PhysRev.156.470