  Bilayer graphene in a magnetic field supports eight zero-energy Landau
levels, which, as a tunable band gap develops, split 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, with focus
on revealing further controllable features in bilayer graphene. The half-filled
pseudo-zero-mode levels support, via orbital level mixing, charge carriers with
nonzero electric moment, which would lead to field-induced level splitting and
the current-induced quantum Hall effect. It is shown that the Coulomb
interaction enhances the effect of the in-plane field and their interplay leads
to rich spectra of collective excitations, pseudospin waves, accessible by
microwave experiments; also a duality in the excitation spectra is revealed.
