Superconductivity and the High-T_c materials

Abstract

Superconductivity, one of the most fascinating phenomena in solid-state physics, was discovered in 1911 by Kamerlingh Onnes [14.1], but it was not until 1957 that a satisfactory microscopic theory of the effect became available, i.e., the one by Bardeen, Cooper and Schrieffer (BCS) [14.2]. The major obstacle theorists were faced with earlier can be summarized as follows. The superconducting transition temperature T _c is usually of the order of 10 K, which corresponds to an energy of order 1 meV (we are not considering for the moment the more recent high-temperature superconductors). Provided that superconductivity is based on electron correlations and taking into account that the correlation energy of electrons in a metal is of the order of 1 eV per electron, is it then necessary to compute that energy to an accuracy of order 1‰ to find a superconducting ground state? This would indeed be an impossible task and eliminate any hope for a microscopic theory. Fortunately, a very special correlation leads to the phenomenon of superconductivity and the treatment of the remaining correlation contributions is unnecessary. All the correlations that are difficult to treat — and thus have been left out — enter the theory only in the form of renormalization parameters. An example are the heavy-fermion systems, in which the characteristic strong correlations manifest themselves in the form of quasiparticle energies; the (pair) correlations responsible for superconductivity are added and treated separately. This explains why reliable calculations of the superconducting transition temperature have so far remained an unsolved problem. They would require a microscopic calculation of those parameters.