  We theoretically study the effects of electron-electron interaction in
twisted bilayer graphene in applied transverse dc electric field. When the
twist angle is not very small, the electronic spectrum of the bilayer consists
of four Dirac cones inherited from each graphene layer. Applied bias voltage
leads to the appearance of two hole-like and two electron-like Fermi surface
sheets with perfect nesting among electron and hole components. Such a band
structure is unstable with respect to exciton band gap opening due to the
screened Coulomb interaction. The exciton order parameter is accompanied by the
spin-density-wave order. The value of the gap depends on the twist angle. More
importantly, it can be controlled by applied bias voltage which opens new
directions in manufacturing of different nanoscale devices.
