Edward McCann

We derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase 2pi. Its high-magnetic-field Landau-level spectrum consists of almost equidistant groups of fourfold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, sigma(xy)(N), which exhibits plateaus at integer values of 4e2/h and has a double 8e2/h step between the hole and electron gases across zero density, in contrast to (4n + 2)e2/h sequencing in a monolayer.

A tight-binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $\ensuremath{\Delta}$ between the conduction and valence bands. In particular, a self-consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density $n$ of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap $\ensuremath{\Delta}(n)$. We discuss the influence of a finite asymmetry gap $\ensuremath{\Delta}(0)$ at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect.

Because of the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalization and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks $\mathbf{p}\ensuremath{\rightarrow}\ensuremath{-}\mathbf{p}$ symmetry of the Fermi line in each valley) suppresses antilocalization, while intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking a ``hidden'' valley symmetry of the system.

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski–Weiss–McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.