Electronic properties of monolayer and bilayer graphene

TL;DR

This paper reviews the electronic properties of monolayer and bilayer graphene, focusing on their low-energy Hamiltonians, quantum Hall effects, and tunable band gaps under electric fields.

Contribution

It derives low-energy Hamiltonians for monolayer and bilayer graphene, explaining their chiral fermions and quantum Hall phenomena, and models the tunable band gap in bilayer graphene.

Findings

Massless Dirac fermions in monolayer graphene

Massive chiral fermions in bilayer graphene

Tunable band gap in bilayer graphene under electric field

Abstract

The tight-binding model of electrons in graphene is reviewed. We derive low-energy Hamiltonians supporting massless Dirac-like chiral fermions and massive chiral fermions in monolayer and bilayer graphene, respectively, and we describe how their chirality is manifest in the sequencing of plateaus observed in the integer quantum Hall effect. The opening of a tuneable band gap in bilayer graphene in response to a transverse electric field is described, and we explain how Hartree theory may be used to develop a simple analytical model of screening.