  Tuning interactions between Dirac states in graphene has attracted enormous
interest because it can modify the electronic spectrum of the two-dimensional
material, enhance electron correlations, and give rise to novel
condensed-matter phases such as superconductors, Mott insulators, Wigner
crystals and quantum anomalous Hall insulators. Previous works predominantly
focus on the flat band dispersion of coupled Dirac states from different
graphene layers. In this work, we propose a new route to realizing flat band
physics in monolayer graphene under a periodic modulation from substrates. We
take gaphene/SiC heterostructure as a role model and demonstrate experimentally
the substrate modulation leads to Dirac fermion cloning and consequently, the
proximity of the two Dirac cones of monolayer graphene in momentum space. Our
theoretical modeling captures the cloning mechanism of Dirac states and
indicates that flat bands can emerge at certain magic lattice constants of
substrate when the period of modulation becomes nearly commensurate with the
$(\sqrt{3}\times\sqrt{3})R30^{\circ}$ supercell of graphene. The results show
that the epitaxial monolayer graphene is a promising platform for exploring
exotic many-body quantum phases arising from interactions between Dirac
electrons.
