  We study the electronic properties of AA-stacked bilayer graphene in a
transverse electric field. The strong on-site Coulomb repulsion stabilizes the
antiferromagnetic order in such a system. The antiferromagnetic order is
suppressed by the transverse bias voltage, at least partially. The inter-plane
Coulomb repulsion and non-zero voltage stabilize an exciton order parameter.
The exciton order parameter coexists with the antiferromagnetism and can be as
large as several tens of meV for realistic values of the bias voltage and
interaction constants. The application of a transverse bias voltage can be used
to control the transport properties of the bilayer.
