Coupled electron-impurity and electron-phonon systems as trivial non-Fermi liquids

TL;DR

This paper analyzes electron systems interacting with impurities and phonons in 2D and 3D, revealing non-Fermi liquid behavior characterized by non-Lorentzian spectral functions and non-Fermi momentum distributions at finite temperatures.

Contribution

It provides a detailed finite-temperature perturbation theory analysis showing that coupled electron-impurity and electron-phonon systems are trivial non-Fermi liquids with well-understood properties.

Findings

Spectral functions are highly non-Lorentzian.

Momentum distribution functions deviate from Fermi functions at all temperatures.

The system exhibits non-Fermi liquid behavior in both 2D and 3D.

Abstract

We consider an electron gas, both in two (2D) and three (3D) dimensions, interacting with quenched impurities and phonons within leading order finite-temperature many body perturbation theories, calculating the electron self-energies, spectral functions, and momentum distribution functions at finite temperatures. The resultant spectral function is in general highly non-Lorentzian, indicating that the system is not a Fermi liquid in the usual sense. The calculated momentum distribution function cannot be approximated by a Fermi function at any temperature, providing a rather simple example of a non-Fermi liquid with well-understood properties.