Remarks on the tight-binding model of graphene

Cristina Bena (1, 2) , Gilles Montambaux (1)

1 LPS - Laboratoire de Physique des Solides
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We address a simple but fundamental issue arising in the study of graphene, as well as of other systems that have a crystalline structure with more than one atom per unit cell. For these systems, the choice of the tightbinding basis is not unique. For monolayer graphene two bases are widely used in the literature. While the expectation values of operators describing physical quantities should be independent of basis, the form of the operators may depend on the basis, especially in the presence of disorder or of an applied magnetic field. Using an inappropriate form of certain operators may lead to erroneous physical predictions. We discuss the two bases used to describe monolayer graphene, as well as the form of the most commonly used operators in the two bases. We repeat our analysis for the case of bilayer graphene.

Mots clés: graphene; crystal structure; Hamiltonian; state operators; density operator; quantization

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]; Cristallographie

Cristina Bena, Gilles Montambaux. Remarks on the tight-binding model of graphene. New Journal of Physics, 2009, 11, pp.095003. ⟨10.1088/1367-2630/11/9/095003⟩. ⟨cea-00442938⟩