Nonequilibrium effects in the tunneling conductance spectra of small metallic particles

TL;DR

This paper investigates how nonequilibrium effects influence the tunneling conductance spectra of small metallic particles, revealing complex resonance structures caused by electron interactions and excitations under high bias conditions.

Contribution

It provides a detailed analysis of nonequilibrium phenomena in metallic grains, including Coulomb and pairing interactions, explaining the origin of resonance substructures in conductance spectra.

Findings

Resonance peaks form clusters or substructures under high bias.

Normal grains' resonances relate to excited single-electron states.

Superconducting grains show nonequilibrium gapless excitations.

Abstract

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.