Incommensurate intervalley coherent states in ABC graphene: Collective modes and superconductivity

Here, the authors identify incommensurate intervalley fluctuations between concentric hole and electron pockets as the primary particle-hole instability in hole-doped $A\phantom{\rule{0}{0ex}}B\phantom{\rule{0}{0ex}}C$-graphene's half-metallic state. At intermediate densities, these fluctuations lead to a low-temperature superconducting instability with a sign-changing $s$-wave order parameter as revealed through a generalized RPA analysis. Closer to charge neutrality, the system develops finite-momentum intervalley coherent order, followed by a transition to a valley polarized state.