ABSTRACT
This chapter examines some situations where non-local relationships are important and reviews the various characteristic lengths of superconductors. It develops an alternative form of bcs theory, worked out by Gor'kov, de Gennes and others. BCS theory in its original form was designed to handle a uniform, translationally invariant superconductor containing excitations of definite momentum. The Bcs kernel used so far has been that for a clean superconductor in which the excitations occupy plane-wave states. In extending the treatment to materials with a large number of scattering centres it is helpful to look into the details of the calculation of the kernel. In the superconductor, by contrast, the magnetic field is a static perturbation which produces permanent current elements. In considering the response of superconductors to high-frequency fields, there are many situations, especially with conventional superconductors, where the non-locality of the response is important, and calculations must be based on the full Mattis-Bardeen equation.
