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

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 $T_{\text{c}}$ is obtained. When only the breathing phonon is considered, $T_{\text{c}}$ is the same as that of the one-band model. On the other hand, when Jahn–Teller phonons are active, $T_{\text{c}}$ 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. ©2010

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