Interactions and phase transitions on graphene's honeycomb lattice

Abstract

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and of the magnetic field are discussed.

four pages, one figure; few typos corrected, references added

References in corpus (6)

• Electric Field Effect in Atomically Thin Carbon Films
• Unconventional Integer Quantum Hall effect in graphene
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
• Effective theory of high-temperature superconductors
• Strain induced correlation gaps in carbon nanotubes

Cited by in corpus (45)

• The electronic properties of graphene
• Topological Mott Insulators
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Density waves and Cooper pairing on the honeycomb lattice
• Gauge field induced by ripples in graphene
• Quantum critical point in graphene approached in the limit of infinitely strong Coulomb interaction
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Inverse magnetic catalysis in dense holographic matter
• Lattice field theory simulations of graphene
• Theory of integer quantum Hall effect in graphene
• Quantum Critical Behaviour in a Graphene-like Model
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
• Supercritical Coulomb center and excitonic instability in graphene
• Coulomb interaction in graphene: Relaxation rates and transport
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• Renormalization group approach to 2D Coulomb interacting Dirac fermions with random gauge potential
• Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
• UV fixed-point structure of the three-dimensional Thirring model
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Effect of electron-electron interaction on the Fermi surface topology of doped graphene
• Renormalization group flow of quartic perturbations in graphene: Strong coupling and large-N limits
• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• Dynamical Mean Field Study of The Dirac Liquid
• Spin-flip excitations, spin waves, and magneto-excitons in graphene Landau levels at integer filling factors
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Lattice gauge theory model for graphene
• Quantum critical scaling in magnetic field near the Dirac point in graphene
• Toward theory of quantum Hall effect in graphene
• Sensory Organ like Response of Zigzag Edge Graphene Nanoribbons
• Tomonaga-Luttinger liquid parameters of magnetic waveguides in graphene
• Magnetic field induced semimetal-to-canted-antiferromagnet transition on the honeycomb lattice
• Gap generation for Dirac fermions on Lobachevsky plane in a magnetic field
• Quantum Hall plateau transition in the lowest Landau level of disordered graphene
• Properties of A Class of Topological Phase Transition
• Estimates of Effective Hubbard Model Parameters for C20 isomers
• Competition between excitonic gap generation and disorder scattering in graphene
• Explanation for the isotropy of the Dirac cone in graphene
• Charge density wave in graphene: magnetic-field-induced Peierls instability