Weak-Coupling Theory for Multiband Superconductivity Induced by Jahn-Teller Phonons

TL;DR

This paper develops a weak-coupling theory for multiband superconductivity mediated by Jahn-Teller phonons, showing that these phonons significantly enhance the transition temperature, with implications for materials like iron pnictides.

Contribution

It introduces a weak-coupling framework for multiband superconductivity with Jahn-Teller phonons, deriving a BCS-like formula and highlighting the enhancement of $T_c$ due to interband attraction.

Findings

Jahn-Teller phonons significantly increase $T_c$ in multiband systems.

The model reproduces $T_c$ similar to one-band systems with only breathing phonons.

Interband attraction is crucial for $T_c$ enhancement in the presence of Jahn-Teller phonons.

Abstract

Emergence of superconductivity in a two-band system coupled with breathing and Jahn-Teller phonons is discussed in a weak-coupling limit. With the use of a standard quantum mechanical procedure, the phonon-mediated attraction is derived. From the analysis of the model including such attraction, a BCS-like formula for a superconducting transition temperature $T_{\rm c}$ is obtained. When only the breathing phonon is considered, $T_{\rm c}$ is the same as that of the one-band model. On the other hand, when Jahn-Teller phonons are active, $T_{\rm c}$ is significantly enhanced by the interband attraction even within the weak-coupling limit. Relevance of the present result to actual materials such as iron pnictides is briefly commented.