Electromagnetic response and pseudo-zero-mode Landau levels of bilayer graphene in a magnetic field

The electromagnetic response of bilayer graphene in a magnetic field is studied in comparison to that of monolayer graphene. Both types of graphene turn out to be qualitatively quite similar in dielectric and screening characteristics, especially those deriving from vacuum fluctuations, but the effect is generally much more sizable for bilayers. The presence of the zero-(energy-)mode Landau levels is a feature specific to graphene. In bilayers, unlike in monolayers, the effect of the zero-mode levels becomes visible and even dominant in density response as an externally controllable band gap develops. It is pointed out that the splitting of nearly degenerate pseudo-zero-mode levels at each valley, which are specific to bilayer graphene, is controlled by an applied inplane electric field or by an injected current. In addition, a low-energy effective gauge theory of bilayer graphene is constructed.