Superconducting Energy Gap in Hole-Doped Graphene Beyond the Migdal's Theory

Abstract

In this work, we analyze the impact of non-adiabatic effects on the superconducting energy gap in hole-doped graphene. By using the Eliashberg formalism beyond Migdal's theorem, we present that non-adiabatic effects strongly influence the superconducting energy gap in the exemplary boron-doped graphene. In particular, non-adiabatic effects, as represented by the first-order vertex corrections to the electron-phonon interaction, supplement the Coulomb depairing correlations and suppress the superconducting state. In summary, the obtained results confirm previous studies on superconductivity in two-dimensional materials and show that the corresponding superconducting phase may be notably affected by non-adiabatic effects.