Nonequilibrium effects in the tunneling conductance spectra of small metallic particles

The tunneling spectra of small metallic grains shows an unusual structure of the differential conductance peaks. Namely, resonance peaks appear in clusters, or develop substructure as the the gate voltage is changed. These features are manifestations of a nonequilibrium behavior which appears when the applied source-drain voltage is sufficiently large. Electron-electron Coulomb interaction as well as an attractive pairing interaction play an important role in determining the magnitude and energy scales of the phenomena. 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. For superconducting grains in the odd charging state, the substructure of the resonance is explained by nonequilibrium ``gapless'' excitations associated with different energy levels occupied by the unpaired electron. The excitations are generated by inelastic cotunneling.