The stacking order of multilayer graphene significantly influences its electronic properties. The rhombohedral stacking sequence is predicted to introduce a flat band, which has high density of states and the enhanced Coulomb interaction between charge carriers, thus possibly resulting in superconductivity, fractional quantum Hall effect, and many other exotic phases of matter. In this work, we comprehensively study the effect of the stacking sequence and interlayer spacing on the electronic structure of four-layer graphene, which was grown on a high crystalline quality 3C-SiC(111) crystal. The number of graphene layers and coverage were determined by low energy electron microscopy. First-principles density functional theory calculations show distinctively different band structures for ABAB (Bernal), ABCA (rhombohedral), and ABCB (turbostratic) stacking sequences. By comparing with angle-resolved photoelectron spectroscopy data, we can verify the existence of a rhombohedral stacking sequence and a nearly dispersionless electronic band (flat band) near the Fermi level. Moreover, we find that the momentum width, bandgap, and curvature of the flat-band region can be tuned by the interlayer spacing, which plays an important role in superconductivity and many other exotic phases of matter.
Keywords: Graphene; flat-band; interlayer spacing; rhombohedral stacking; superconductor.