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

AA-stacked bilayer graphene in an applied electric field: Tunable antiferromagnetism and coexisting exciton order parameter