Spin, spin-orbit, and electron-electron interactions in mesoscopic systems

We review recent theoretical developments about the role of spins, electron-electron interactions, and spin-orbit, coupling in metal nanoparticles and semiconductor quantum dots. For a closed system, in the absence of spill-orbit coupling or of all external magnetic field! electron-electron interactions make it possible to have ground states with Spin S > 1/2. We review here a, theoretical analysis which makes predictions for the probability of finding various values of spin S for all irregular particle in the limit where the number of electron is large but finite. We also present results for the probability distribution of the spacing between successive groundstate energies in such a particle. In a metallic particle with strong spin-orbit interact ions, for odd electron number, the groundstate has a Kramers' degeneracy, which is split linearly by a weak applied magnetic field. The splitting may be characterized by an effective g-tensor whose principal axes and eigenvalues vary from one level to another. Recent calculations have addressed the joint probability distribution, including the anisotropy, of the eigenvalues. The peculiar form of the spin-orbit coupling for a two-dimensional electron system in a GaAs heterostructure or quantum well leads to a strong suppression of spin-orbit effects when the electrons are confined in a small quantum dot. Spin-effeets can be enhanced, however, in the presence of an applied magnetic field parallel to the layer, which may explain recent observations oil fluctuations in the conductances through such dots. We also discuss possible explanations for the experimental observations by Davidovic and Tinkham of a multiplet splitting of the lowest resonance in the tunneling conductance through a, gold nano-partiele.