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

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Cited by in corpus (31)

• Andreev reflection and Klein tunneling in graphene
• The optical conductivity of graphene in the visible region of the spectrum
• Theory of interacting electrons on the honeycomb lattice
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• On the universal AC optical background in graphene
• Coulomb interaction, ripples, and the minimal conductivity of graphene
• Quantum Critical Behaviour in a Graphene-like Model
• Conductivity of suspended and non-suspended graphene at finite gate voltage
• Regarding confinement and dynamical chiral symmetry breaking in QED3
• Dynamics of the particle - hole pair creation in graphene
• Gauge invariance of a critical number of flavours in QED3
• 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
• Spectrum of $\pi$ Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Dirac electrons in graphene-based quantum wires and quantum dots
• Ground-state properties of gapped graphene using the random phase approximation
• Gauge fields and curvature in graphene
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Transport in a Clean Graphene Sheet at Finite Temperature and Frequency
• Berry Curvature in Graphene: A New Approach
• 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
• Vertex renormalization in dc conductivity of doped chiral graphene
• Conductance Through Graphene Bends and Polygons
• Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
• $\bar{\psi }\psi$-condensate in constant magnetic fields
• Robustness of the optical-conductivity sum rule in Bilayer Graphene
• Phase diagram for quantum Hall states in graphene