Increasing flatness of surface bands of multilayer rhombohedral graphite with crystal thickness

Flat bands, where Coulomb repulsion dwarfs bandwidth, hold the potential to realize many correlated electron states in a material. Rhombohedral graphite (RG) hosts an intrinsic flat band near the Fermi level localized on its top and bottom surfaces, in which the density of states is predicted to increase sharply with increasing crystal thickness. Here, we study rhombohedral graphite samples of multiple thicknesses using scanning tunneling microscopy and spectroscopy. We observe a van Hove singularity (vHs) in the density of states of all samples as well as additional peaks corresponding to the onsets of higher-energy bands that have been pushed away from the Fermi level due to interlayer hopping. The relative height of the central vHs to the higher-energy peaks increases with crystal thickness, a result that agrees quantitatively with our tight-binding (TB) calculations. We study the boundary between RG and hexagonal graphite and observe splitting of the flat surface band, an effect which can be described by the inclusion of a stacking fault into our TB model.