Superconductivity in Ultrasmall Grains: Introduction to Richardson's Exact Solution

Abstract

Studies of pairing correlations in ultrasmall metallic grains have commonly been based on a simple reduced BCS-model describing the scattering of pairs of electrons between discrete energy levels that come in time-reversed pairs. This model has an exact solution, worked out by Richardson in the context of nuclear physics in the 1960s. Here we give a tutorial introduction to his solution, and use it to check the quality of various previous treatments of this model.

10 pages, 1 figure, Submitted to the Proceedings of the NATO ASI "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics", Ankara/Antalya, Turkey, June 1999, Eds. I.O. Kulik and R. Ellialtioglu, Kluwer Ac. Publishers