AB-Stacked Graphenes

The Coulomb excitation behaviors are mainly determined by the electronic structures and geometric symmetries. The 2p_z orbitals of carbon atoms in graphene-related systems, which built the π valence bands and the π^ast conduction bands, are responsible for the electronic excitations lower than the middle frequency (~6-10 eV). The low-lying band structures of layered graphenes strongly depend on the intralayer and interlayer hopping integrals of 2p_z orbitals. The trilayer ABA stacking (Figure 5.1a) exhibits the unusual energy bands, two pairs of parabolic valence and conduction bands and one pair of distorted Dirac-cone structures (Figure 5.1b); the corresponding van Hove singularities are presented in the density of states (DOS) (Figure 5.1c). As verified from the high-resolution angle-resolved photo emission spectroscopy [64,284,285], the distorted Dirac cone could survive in AB-stacked graphene systems with odd layers [64,284]. Also, there exist the special wave functions arising from the specific superpositions of the six tight-binding functions, being directly reflected in the existence/strength of the Coulomb interactions. Band structure and wave functions are directly included in the current calculations.