Relevance of multiband Jahn-Teller effects on the electron-phonon interaction in $A_3$C$_{60}$

TL;DR

This paper investigates how multiband effects influence electron-phonon interactions in $A_3$C$_{60}$ fullerides, revealing that non-degenerate bands and interband scattering significantly impact theoretical models of superconductivity.

Contribution

It demonstrates that assuming perfect degeneracy oversimplifies the electron-phonon interactions, highlighting the importance of multiband effects and non-degeneracy in $A_3$C$_{60}$ compounds.

Findings

Vertex corrections are much smaller than non-crossing terms under perfect degeneracy.

Degenerate band models may not reliably describe real systems.

Interband scattering dominates electron-phonon interactions in these materials.

Abstract

Assessing the effective relevance of multiband effects in the fullerides is of fundamental importance to understand the complex superconducting and transport properties of these compounds. In this paper we investigate in particular the role of the multiband effects on the electron-phonon (el-ph) properties of the $t_{1u}$ bands coupled with the Jahn-Teller intra-molecular $H_g$ vibrational modes in the C$_{60}$ compounds. We show that, assuming perfect degeneracy of the electronic bands, vertex diagrams arising from the breakdown of the adiabatic hypothesis, are one order of magnitude smaller than the non-crossing terms usually retained in the Migdal-Eliashberg (ME) theory. These results permit to understand the robustness on ME theory found by numerical calculations. The effects of the non degeneracy of the $t_{1u}$ in realistic systems are also analyzed. Using a tight-binding model we show that the el-ph interaction is mainly dominated by interband scattering within a single electronic band. Our results question the reliability of a degenerate band modeling and show the importance of these combined effects in the $A_3$C$_{60}$ family.