Implications of the electron-phonon coupling in CuPb₉(PO₄)₆O for superconductivity: an ab initio study

We report ab initio calculations of the electronic and vibrational properties in CuPb₉(PO₄)₆O, including the electron-phonon coupling strength via strong-coupling Migdal-Eliashberg theory. We verify the presence of appealing flat electronic bands near the Fermi level, a strong hybridization between the Cu 3d and O 2p states, and soft low-energy phonons, which can suggest high-temperature superconducting behavior. However, the electron-phonon coupling strength appears insufficient to overcome the Coulomb repulsion between an electron pair and thus does not support high-temperature superconductivity in CuPb₉(PO₄)₆O via the conventional electron-phonon Migdal-Eliashberg mechanism. Even neglecting Coulomb repulsion of the electron pair we find this electron-phonon coupling suggests a superconducting transition temperature less than 2 K.