Electron-phonon interaction in the lamellar cobaltate Na$_x$CoO$_2$

TL;DR

This paper investigates how the electron-phonon interaction in Na$_x$CoO$_2$ varies with sodium doping, combining theoretical calculations and experimental data to understand phonon behavior and its potential role in the material's properties.

Contribution

It provides a detailed analysis of the doping dependence of electron-phonon interactions for specific phonon modes in Na$_x$CoO$_2$, integrating theory with Raman spectroscopy results.

Findings

The $A_{1g}$ phonon mode frequency shifts with doping as predicted by electron-phonon feedback.

The $E_{1g}$ mode shows no frequency renormalization due to momentum-dependent coupling.

Theoretical calculations align with experimental observations of phonon behavior across doping levels.

Abstract

We study theoretically and experimentally the dependence of the electron-phonon interaction in Na$_x$CoO$_2$ on the sodium concentration $x$. For the two oxygen phonon modes found in Raman experiments, $A_{1g}$ and $E_{1g}$, we calculate the matrix elements of the electron-phonon interaction. Analyzing the feedback effect of the conduction electrons on the phonon frequency we compare the calculated and experimentally observed doping dependence of the $A_{1g}$ mode. Furthermore, due to the momentum dependence of the electron-phonon coupling for the $E_{1g}$ symmetry we find no renormalization of the corresponding phonon frequency which agrees with experiment. Our results shed light on the possible importance of the electron-phonon interaction in this system.