Phonon-mediated unconventional superconductivity in rhombohedral stacked multilayer graphene

Understanding the origin of superconductivity in correlated two-dimensional materials is a key step in leveraging material engineering techniques for next-generation nanoscale devices. While it is widely accepted that phonons fluctuations only mediate conventional (s-wave) superconductivity, the common phenomenology of superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well as in a large family of graphene-based moir & eacute; systems, suggests a common superconducting mechanism across these platforms. In particular, in all these platforms some superconducting regions violate the Pauli limit, indicating unconventional superconductivity, naively ruling out conventional phonon-mediated pairing as the underlying mechanism. Here we combine first principles simulations with effective low-energy theories to investigate the superconducting mechanism and pairing symmetry in rhombohedral stacked graphene multilayers. We find that phonon-mediated superconductivity explains the main experimental findings, namely the displacement field and doping level dependence of the critical temperature, and the presence of two superconducting regions with different pairing symmetries that depend on the parent normal state. In particular, we find that intra-valley phonon scattering favors a triplet f-wave pairing when combined with electronic correlations stabilizing a spin- and valley-polarized normal state. We also propose a so far unexplored superconducting region at higher hole doping densities nh approximate to 4 x 1012 cm-2, and demonstrate how this highly hole-doped regime can be reached in heterostructures consisting of monolayer alpha-RuCl3 and rhombohedral trilayer graphene. Our findings promote phonon-mediated pairing as a strong contender to explain superconductivity across a wide range of graphene platforms, and demonstrate that phonons can, in fact, stabilize unconventional superconducting orders.