Ac Conductivity of Graphene:. from TightBinding Model to 2 + 1DIMENSIONAL Quantum Electrodynamics
Abstract
We consider the relationship between the tightbinding Hamiltonian of the twodimensional 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.
 Publication:

International Journal of Modern Physics B
 Pub Date:
 2007
 DOI:
 10.1142/S0217979207038022
 arXiv:
 arXiv:0706.3016
 Bibcode:
 2007IJMPB..21.4611G
 Keywords:

 Graphene;
 Dirac theory;
 chirality;
 symmetry;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Phenomenology
 EPrint:
 46 pages, wsijmpb, 7 EPS figures