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Wigner crystal and bubble phases in graphene in the quantum Hall regime
Graphene, a single free-standing sheet of graphite with honeycomb lattice
structure, is a semimetal with carriers that have linear dispersion. A
consequence of this dispersion is the absence of Wigner crystallization in
graphene, since the kinetic and potential energies both scale identically with
the density of carriers. We study the ground state of graphene in the presence
of a strong magnetic field focusing on states with broken translational
symmetry. Our mean-field calculations show that at integer fillings a uniform
state is preferred, whereas at non-integer filling factors Wigner crystal
states (with broken translational symmetry) have lower energy. We obtain the
phase diagram of the system. We find that it is qualitatively similar to that
of quantum Hall systems in semiconductor heterostructures. Our analysis
predicts that non-uniform states, including Wigner crystal state, will occur in
graphene in the presence of a magnetic field and will lead to anisotropic
transport in high Landau levels.Comment: New references added; 9 pages, 9 figures, (paper with high-resolution
images is available at http://www.physics.iupui.edu/yogesh/graphene.pdf
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