The Eliashberg Function of Strong Coupling Superconductivity and Lifetime Broadening in Graphene

This paper theoretically investigates the lifetime broadening in graphene using the Eliashberg function of strong coupling superconductivity theory. The normal state lifetime broadening is calculated using the low-temperature limit, while the superconducting-state lifetime broadening is obtained using both low-temperature and low-frequency approximations. In both cases, the Eliashberg function is employed, considering only phonon emissions and electron-phonon interactions on the Fermi surface, with the quasi-elastic approximation term absent in the resulting expression. Notably, the results suggest that this lifetime broadening is highly dependent on the perturbation potential caused by electron-phonon interactions, highlighting the critical role of these interactions in shaping the material’s electronic characteristics. Furthermore, the scattering process dominates the lifetime broadening contribution in the superconducting state, particularly under conditions where phonon-mediated interactions are enhanced. This finding provides valuable insights into the intricate behavior of graphene in superconducting regimes, offering a theoretical framework that advances our understanding of its properties and potential applications.