  We employ a functional renormalization group approach to ascertain the
pairing mechanism and symmetry of the superconducting phase observed in
rhombohedral trilayer graphene. Superconductivity in this system occurs in a
regime of carrier density and displacement field with a weakly distorted
annular Fermi sea. We find that repulsive Coulomb interactions can induce
electron pairing on the Fermi surface by taking advantage of momentum-space
structure associated with the finite width of the Fermi sea annulus. The
degeneracy between spin-singlet and spin-triplet pairing is lifted by
valley-exchange interactions that strengthen under the RG flow and develop
nontrivial momentum-space structure. We find that the leading pairing
instability is $d$-wave-like and spin-singlet, and that the theoretical phase
diagram versus carrier density and displacement field agrees qualitatively with
experiment.
