Dirac Fermion Cloning, Moire Flat Bands, and Magic Lattice Constants in Epitaxial Monolayer Graphene

Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D 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 twisted graphene layers. In this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moire flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the (3 x 3)R30o\[(\sqrt 3 \; \times \;\sqrt 3 )R{30<^>o}\] supercell of graphene. The results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.