Optical sum increase due to electron undressing

TL;DR

This paper investigates how electron-phonon interactions influence the optical spectral weight in metals, revealing that changes in phonon frequency can lead to electron undressing and increased optical sum, aligning with experimental observations in cuprates.

Contribution

It models the impact of electron-phonon coupling on the optical sum rule, showing how phonon frequency shifts affect electron kinetic energy and optical spectral weight.

Findings

Hardening of phonon frequency increases optical sum

Electron undressing correlates with phase transition effects

Model aligns with experimental data in cuprate superconductors

Abstract

For a system with a fixed number of electrons, the total optical sum is a constant, independent of many-body interactions, of impurity scattering and of temperature. For a single band in a metal, such a sum rule is no longer independent of the interactions or temperature, when the dispersion and/or finite bandwidth is accounted for. We adopt such a model, with electrons coupled to a single Einstein oscillator of frequency $\omega_{E}$, and study the optical spectral weight. The optical sum depends on both the strength of the coupling and on the characteristic phonon frequency, $\omega_{E}$. A hardening of $\omega_{E}$, due, for example, to a phase transition, leads to electron undressing and translates into a decrease in the electron kinetic energy and an increase in the total optical sum, as observed in recent experiments in the cuprate superconductors.