  The electromagnetic response of bilayer graphene in a magnetic field is
studied in comparison with 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, 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.
