Electronic excitations and the tunneling spectra of metallic nanograins

TL;DR

This paper develops a microscopic mean-field theory to analyze electronic excitations in metallic nanograins, revealing strong disorder-induced fluctuations and potential for higher spectral resonance densities in tunneling spectra.

Contribution

It introduces a new mean-field approach to study electronic excitations and their effects on tunneling spectra in metallic nanograins, highlighting disorder effects and non-equilibrium phenomena.

Findings

Electronic energy response fluctuates strongly due to disorder.

Sample dependence significantly affects tunneling spectra.

Higher spectral densities of resonances are possible with non-equilibrium populations.

Abstract

Tunneling-induced electronic excitations in a metallic nanograin are classified in terms of {\em generations}: subspaces of excitations containing a specific number of electron-hole pairs. This yields a hierarchy of populated excited states of the nanograin that strongly depends on (a) the available electronic energy levels; and (b) the ratio between the electronic relaxation rate within the nano-grain and the bottleneck rate for tunneling transitions. To study the response of the electronic energy level structure of the nanograin to the excitations, and its signature in the tunneling spectrum, we propose a microscopic mean-field theory. Two main features emerge when considering an Al nanograin coated with Al oxide: (i) The electronic energy response fluctuates strongly in the presence of disorder, from level to level and excitation to excitation. Such fluctuations produce a dramatic sample dependence of the tunneling spectra. On the other hand, for excitations that are energetically accessible at low applied bias voltages, the magnitude of the response, reflected in the renormalization of the single-electron energy levels, is smaller than the average spacing between energy levels. (ii) If the tunneling and electronic relaxation time scales are such as to admit a significant non-equilibrium population of the excited nanoparticle states, it should be possible to realize much higher spectral densities of resonances than have been observed to date in such devices. These resonances arise from tunneling into ground-state and excited electronic energy levels, as well as from charge fluctuations present during tunneling.