On the visibility of electron-electron interaction effects in field emission spectra

TL;DR

This paper analyzes how electron-electron interactions influence field emission spectra, focusing on the high-energy tail, and predicts the energy range where second-order tunneling dominates, with applications to Luttinger liquids and nanotubes.

Contribution

It provides a detailed analysis of the visibility of electron-electron interaction effects in field emission spectra, including higher-order contributions and thermal effects, with specific predictions for certain materials.

Findings

Second-order tunneling dominates in a specific energy window.

Higher-order contributions and thermal smearing can obscure interaction effects.

Application to Luttinger liquids and carbon nanotubes demonstrates practical relevance.

Abstract

One of the most convenient methods to obtain information about the energy distribution function of electrons in conducting materials is the measurement of the energy resolved current $j(\omega)$ in field emission (FE) experiments. Its high energy tail $j_>(\omega)$ (above the Fermi edge) contains invaluable information about the nature of the electron--electron interactions inside the emitter. Thus far, $j_>(\omega)$ has been calculated to second order in the tunnelling probability, and it turns out to be divergent toward the Fermi edge for a wide variety of emitters. The extraction of the correlation properties from real experiments can potentially be obscured by the eventually more divergent contributions of higher orders as well as by thermal smearing around $E_F$. We present an analysis of both factors and make predictions for the energy window where only the second order tunnelling events dominate the behaviour of $j_>(\omega)$. We apply our results to the FE from Luttinger liquids and single-wall carbon nanotubes.