Abstract
Since the discovery by Kamerlingh Onnes in 1911 superconductivity has remained an important phenomenon in solid state physics with continuing discoveries. The explanation of the superconductivity phenomenon was given by the most elegant BCS theory of Bardeen, Cooper, and Schrieffer in 1957. The formation of Cooper pairs results from an effective attractive phonon-mediated interaction between two electrons with opposite spin near the Fermi surface. The BCS theory provided justification to the successful phenomenological Ginzburg–Landau theory from 1950. We discuss the BCS theory, Josephson tunneling of Cooper pairs between tunnel junctions, and the McMillan equation for the superconducting transition temperature and use this for its pressure dependence and for superconductivity in amorphous metals. We also discuss the Eliashberg theory treating electrons and phonons in superconductors on the same footing. Furthermore, we also discuss the high transition temperature (cuprate) superconductors for which the Cooper pair glue is still debated and for which the repulsive coupling yields an order parameter of d-symmetry. Interesting behavior of various superconducting nanostructures (e.g., system of quantum dots) is discussed. This is a corrected and extended version of the chapter (Bennemann, 2005).
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