Chiral finite-momentum superconductivity in the tetralayer graphene

Motivated by the recent discovery of superconductivity in tetralayer graphene, we investigate the pairing mechanism arising from density-density interactions within the random phase approximation. This approach successfully highlights the dominance of chiral $p$-wave pairing between electrons with the same spin and valley at low electron 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 nematic zero-momentum superconductivity, with its transition temperature constrained by the pairing strength. Additionally, we delve into the exotic features of chiral finite-momentum superconductivity, underscoring its potential significance for realizing a charge-4e exotic metal with time-reversal symmetry.