Electron-electron Interactions in ABC-stacked Multilayer Graphene

The electronic band structures of ABC-stacked multilayer graphene systems are obtained by the tight-binding calculation and the density function theory. We predict that the electron- electron interactions drive the neutral graphene multilayer systems to pseudospin magnets in which the charge density contribution spontaneously shifts to either the top or the bottom layers, based on the HF and PRG calculations. We show that the spin and valley degrees of freedom enhance the instabilities. We investigate the influence on the broken symmetry phase by the trigonal warping, the external electric field and the number of coupled graphene layers.