  We study the emergence of superconductivity in rhombohedral trilayer graphene
due purely to the long-range Coulomb repulsion. This
repulsive-interaction-driven phase in rhombohedral trilayer graphene is
significantly different from those found in twisted bilayer and trilayer
graphenes. In the latter case, the nontrivial momentum-space geometry of the
Bloch wavefunctions leads to an effective attractive electron-electron
interaction; this allows for less modulated order parameters and for
spin-singlet pairing. In rhombohedral trilayer graphene, we instead find
spin-triplet superconductivity with critical temperatures up to 0.15 K. The
critical temperatures strongly depend on electron filling and peak where the
density of states diverge. The order parameter shows a significant modulation
within each valley pocket of the Fermi surface.
