Interactions and superconductivity in moiré and non-moiré graphene multilayers.

The discovery of correlated phases and superconductivity in moiré and non-moiré graphene multilayers, such as twisted bilayer graphene (TBG), twisted double-bilayer graphene (TDBG), rhombohedral trilayer graphene (RTG) and Bernal bilayer graphene (BBG), has sparked a profound interest in the role that electronic interactions play in these materials. This study focuses on the impact of electron-electron interactions, particularly on superconductivity. Based on a Kohn-Luttinger-like mechanism, we consider the screening of the Coulomb potential due to the effect of electron-hole excitations, plasmons, and electron-phonon interactions in the random phase approximation. The effective Coulomb interaction serves as the pairing glue of the superconducting instability. For untwisted systems superconductivity driven by electronic interactions exhibits critical temperatures ranging from tens to hundreds of millikelvin with spin-triplet, f-wave order parameters. Electron-phonon interactions do not significantly alter these results. In contrast, in twisted systems the electron-phonon interactions are required to achieve experimentally consistent superconductivity, with Umklapp processes playing a key role. The agreement between theoretical predictions and experimental data across three orders of magnitude in the critical temperature indicates that electron interactions are crucial to the superconducting behavior in both twisted and untwisted graphene multilayers.