Nonequilibrium Effects in the Funneling Conductance Spectra of Small Metallic Particles

Recent experiments on the tunneling spectra of small metallic grains revealed an un- usual structure of the differential conductance peaks. The peaks appear in clusters, or develop a substructure as the gate voltage changes. These features are manifestations of nonequilibrium behavior. Electron-electron interactions play an important role in determining the magnitude and the energy scales of the phenomenon. For normal grains, each cluster of resonances is identified with one excited single-electron state of the metal particle, shifted as a result of the different nonequilibrium occupancy configurations of the other single-electron states. Assuming the underlying classical dynamics of the electrons to be chaotic, the typical shift is 5/9 where fi is the single particle mean level spacing and g is the dimensionless conductance of the grain. For superconducting grains in the odd charging state, the substructure of the first resonance is explained by nonequilibrium 'gapless' excitations associated with different energy levels occupied by the unpaired electron. These excitations are generated by inelastic co tunneling