Tunneling through metallic quantum dots

We discuss single-electron tunneling measurements at dilution refrigerator temperatures on metallic grains, sufficiently small that the quantum levels of the conduction electrons can be resolved. These measurements directly r eveal the energy eigenvalues of the electrons in a grain that typically con tains a few thousand conduction electrons. Such measurements were first car ried out a few years ago;by Ralph, et al. on nanograins of Al. More recentl y, this work has been extended to measurements on nanoparticles of the heav y metal Au by Davidovic and on nanoparticles of alloys of Al and Au by Sali nas, et al. This more recent work has pointed up the need to go beyond the simplest independent-electron model, to include the Coulomb interaction bet ween electrons and also nonequilibrium electron populations. These interact ions cause the energy levels to merge into a continuum above the Thouless e nergy and can cause a single quasiparticle level to show up as a cluster of resonances. The strong spin-orbit interaction in Au can cause levels to sp lit in magnetic fields with a g-factor of similar to 0.3, instead of the fr ee electron g = 2. In addition, there is evidence for a proliferation of lo ur-lying energy levels suggestive of system spin values greater than 1/2 in duced by the exchange interaction. This paper will review the evolving prog ress that has been made in interpreting these observations.