Phonon-Mediated Superconductivity near Phase Boundaries in Rhombohedral Multilayer Graphene

Abstract: The recent observation of superconductivity in untwisted multilayer graphene has sparked intense interest in its microscopic origin. As the displacement field and carrier density are varied, superconductivity emerges in several distinct regions with different temperature and magnetic-field responses. This behavior has been attributed to the presence of distinct electronic phases, raising the possibility that different superconducting regions originate from different microscopic mechanisms. While purely electronic pairing mechanisms have been extensively explored, an in-depth examination of phonon-mediated superconductivity is still missing. Here, we solve the coupled selfconsistent Migdal-Eliashberg equations using input from first-principles calculations and incorporating interaction-driven symmetry breaking of the electronic ground state. Varying the carrier density and displacement field, we reproduce the experimentally observed superconducting regions with comparable superconducting properties such as gap and $T_c$ and predict additional, as-yet undiscovered superconducting phases. Our findings exemplify that several superconductivity regions in rhombohedral graphene can be satisfactorily explained by phonon-mediated pairing.