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. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2011-12-4452 |
| Date | 06 February 2012 |
| Creators | Zhang, Fan, 1983- |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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