AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics

Abstract

We consider the relationship between the tight-binding Hamiltonian of the two-dimensional honeycomb lattice of carbon atoms with nearest neighbor hopping only and the 2+1 dimensional Hamiltonian of quantum electrodynamics which follows in the continuum limit. We pay particular attention to the symmetries of the free Dirac fermions including spatial inversion, time reversal, charge conjugation and chirality. We illustrate the power of such a mapping by considering the effect of the possible symmetry breaking which corresponds to the creation of a finite Dirac mass, on various optical properties. In particular, we consider the diagonal AC conductivity with emphasis on how the finite Dirac mass might manifest itself in experiment. The optical sum rules for the diagonal and Hall conductivities are discussed.

46 pages, ws-ijmpb, 7 EPS figures; final version published in IJMPB

References in corpus (18)

• Electric Field Effect in Atomically Thin Carbon Films
• Two Dimensional Atomic Crystals
• The structure of suspended graphene sheets
• Room-Temperature Quantum Hall Effect in Graphene
• Substrate-induced band gap opening in epitaxial graphene
• Unconventional Integer Quantum Hall effect in graphene
• Magneto-optical conductivity in Graphene
• Infrared spectroscopy of Landau levels in graphene
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Sum Rules for the Optical and Hall Conductivity in Graphene
• Chirality and Correlations in Graphene
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene
• Charge and Spin Transport at the Quantum Hall Edge of Graphene
• Optical-conductivity sum rule in cuprates and unconventional charge density waves: a short review
• Optical signatures of electron correlations in the cuprates

Cited by in corpus (11)

• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Optical properties of graphene: the Fermi liquid approach
• The infrared conductivity of graphene
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Transport in a Clean Graphene Sheet at Finite Temperature and Frequency
• Toward theory of quantum Hall effect in graphene
• Spectroscopic Signatures of Massless Gap Opening in Graphene
• Massive Dirac fermions and the zero field quantum Hall effect
• $\bar{\psi }\psi$-condensate in constant magnetic fields
• Robustness of the optical-conductivity sum rule in Bilayer Graphene