  Artificial lattices have served as a platform to study the physics of
unconventional superconductivity. We study semiconductor artificial graphene --
a honeycomb superlattice imposed on a semiconductor heterostructure -- which
hosts the Dirac physics of graphene but with a tunable periodic potential
strength and lattice spacing, allowing control of the strength of the
electron-electron interactions. We demonstrate a new mechanism for
superconductivity due to repulsive interactions which requires a strong lattice
potential and a minimum doping away from the Dirac points. The mechanism relies
on the Berry phase of the emergent Dirac fermions, which causes oppositely
moving electron pairs near the Dirac points to interfere destructively,
reducing the Coulomb repulsion and thereby giving rise to an effective
attraction. The attractive component of the interaction is enhanced by a novel
antiscreening effect which, in turn, increases with doping; as a result there
is a minimum doping beyond which superconducting order generically ensues. The
dominant superconducting state exhibits a spatially modulated gap with chiral
$p$-wave symmetry. Microscopic calculations suggest that the possible critical
temperatures are large relative to the low carrier densities, for a range of
experimentally realistic parameters.
