Spectroscopy of discrete energy levels in ultrasmall metallic grains

We review recent experimental and theoretical work on ultrasmall metallic g rains, i.e. grains sufficiently small that the conduction electron energy s pectrum becomes discrete, The discrete excitation spectrum of an individual grain can be measured by the technique of single-electron tunneling spectr oscopy: the spectrum is extracted from the current-voltage characteristics of a single-electron transistor containing the grain as central island. We review experiments studying the influence on the discrete spectrum of super conductivity, nonequilibrium excitations, spin-orbit scattering and ferroma gnetism. We also review the theoretical descriptions of these phenomena in ultrasmall grains, which require modifications or extensions of the standar d bulk theories to include the effects of level discreteness. (C) 2001 Else vier Science B.V. All rights reserved.