Electronic correlations in few layer graphene
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In this thesis we investigate the electronic band structures and the correlations in chirally (ABC) stacked N-layer graphene with N ≥ 2. We use ab initio density-functional theory and k · p theory to fit the parameters of a p-band tightbinding model. External potential differences between top and bottom layers are strongly screened by charge transfer but still open an energy gap at overall neutrality. Perpendicular magnetic field drives the system into the quantum Hall region with 4N-fold zero energy Landau levels. We predict that Coulomb interactions spontaneously break the SU(4N) symmetry and drive quantum Hall effects at all integer fillings n from −2N to 2N with exotic spin and pseudospin polarizations. Based on mean-field theory and perturbative renormalization group analysis, we predict that the ground state of bilayer graphene spontaneously breaks inversion symmetry for arbitrarily weak electron-electron interactions and conclude that this instability is not suppressed by quantum fluctuations but that, because of trigonal warping, it may occur only in high quality suspended bilayers. Remarkably flat conduction and valence bands that touch at charge neutrality point and Bloch states with large pseudospin chirality combine to make the bilayer graphene gapless band state strongly susceptible to a family of broken symmetry states in which each spinvalley flavor spontaneously transfers charge between layers. We explain how these states are distinguished by their charge, spin, and valley Hall conductivities, by their orbital magnetizations, and by their edge state properties. We further analyze how these competing states are influenced by Zeeman fields that couple to spin and by interlayer electric fields that couple to layer pseudospin, and comment on the possibility of using response and edge state signatures to identify the character of the bilayer ground state experimentally. We demonstrate that similar insulating broken symmetry states and spontaneous topological orders also occur in bilayer’s thicker cousins, chirally stacked multilayer graphene systems.