Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers

We investigate the competition between acoustic phonon mediated superconductivity and long-range Coulomb interaction in moir\'eless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer ABCA-stacked tetralayer graphene. In these phonons can realize, through electron-phonon coupling, both spin-singlet spin-triplet pairings, intra-sublattice pairings ($s$-wave $f$-wave spin-triplet) are dominant channels. Our theory naturally explains distinct recent experimental findings we further predict existence of ABCA arising from interactions. particular, demonstrate that prevails over a wide range doping while exists only narrow near Van Hove singularity Key features our inclusion realistic band structures with appropriate singularities repulsion effects (the so-called ``${\ensuremath{\mu}}^{*}$ effect'') opposing phonon-induced superconducting pairing. also discuss how intervalley scatterings suppress spin-polarized superconductivity. work provides detailed prediction based on electron--acoustic induced superconductivity, which should be investigated future experiments.