Chiral finite-momentum superconductivity in the tetralayer graphene

Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene, we investigate the pairing mechanism arising from the density-density interactions within the random-phase approximation. This approach successfully highlights the dominance of the chiral $p$-wave pairing between electrons with the same spin and valley index at low densities, while also predicting the superconducting range in agreement with experimental findings. Furthermore, we examine the characteristics of distinct superconducting regions: SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations, whereas SC4 displays zero-momentum spin-singlet superconductivity.