  Bilayer graphene in a magnetic field supports eight zero-energy Landau
levels, which, as a tunable band gap develops, evolve into two
nearly-degenerate quartets separated by the band gap. A close look is made into
the properties of such an isolated quartet of pseudo-zero-mode levels at half
filling in the presence of an in-plane electric field and the Coulomb
interaction. The pseudo-zero-mode levels turn out to support, via orbital
mixing, charge carriers with induced electric dipole moment, which lead to
characteristic collective excitations, pseudospin waves, with some controllable
features; possible experimental signals are discussed.
