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Influence of Coulomb interaction on the anisotropic Dirac cone in graphene
Anisotropic Dirac cones can appear in a number of correlated electron
systems, such as cuprate superconductors and deformed graphene. We study the
influence of long-range Coulomb interaction on the physical properties of an
anisotropic graphene by using the renormalization group method and 1/N
expansion, where N is the flavor of Dirac fermions. Our explicit calculations
reveal that the anisotropic fermion velocities flow monotonously to an
isotropic fixed point in the lowest energy limit in clean graphene. We then
incorporate three sorts of disorders, including random chemical potential,
random gauge potential, and random mass, and show that the interplay of Coulomb
interaction and disorders can lead to rich and unusual behaviors. In the
presence of strong Coulomb interaction and a random chemical potential, the
fermion velocities are driven to vanish at low energies and the system turns
out to be an exotic anisotropic insulator. In the presence of Coulomb
interaction and other two types of disorders, the system flows to an isotropic
low-energy fixed point more rapidly than the clean case, and exhibits non-Fermi
liquid behaviors. We also investigate the nonperturbative effects of Coulomb
interaction, focusing on how the dynamical gap is affected by the velocity
anisotropy. It is found that the dynamical gap is enhanced (suppressed) as the
fermion velocities decrease (increase), but is suppressed as the velocity
anisotropy increases.Comment: 24 pages, 17 figure
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