The surface impedance of superconductors and normal conductors: The Mattis-Bardeen theory

The contribution of the Mattis-Bardeen theory to the understanding of the surface impedance of superconductors and normal conductors is reviewed. The early theoretical and experimental studies of the surface impedance of conductors are sketched to provide the context in which the Mattis-Bardeen theory and, independently, the Abrikosov-Gor'kov-Khalatnikov theory were developed. The Mattis-Bardeen theory is described along with the methods for numerical calculation of the surface impedance from their expression for the current density. Extensions to include the effects of anisotropy and strong coupling are briefly discussed. Theory is compared with representative measurements of the surface impedance, demonstrating excellent agreement in absolute magnitude and in the dependences on frequency, temperature, and material parameters.