Spectroscopy of discrete energy levels in ultrasmall metallic grains

We review recent experimental and theoretical work on ultrasmall metallic grains, i.e. grains sufficiently small that the conduction electron energy spectrum becomes discrete. The discrete excitation spectrum of an individual grain can be measured by the technique of single-electron tunneling spectroscopy: 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 superconductivity, nonequilibrium excitations, spin–orbit scattering and ferromagnetism. We also review the theoretical descriptions of these phenomena in ultrasmall grains, which require modifications or extensions of the standard bulk theories to include the effects of level discreteness.