Electronic spectrum of bilayer graphene with broken P-symmetry of both intra- and inter-layers

Abstract Electronic spectra of AA- and AB- graphene bilayers have been investigated for the case when P-symmetry is broken both inside and between the layers. We have focused special attention on the new regime when the band gaps in different layers have opposite signs. For example, the spectrum of AB bilayer is gapless in the case when band gaps of monolayers are equal in magnitude and opposite in sign. At the same time, such a band gap collapse does not occur in the case of the AA bilayer. We have shown that the gate voltage strongly affects the spectrum of gapped AB bilayers. We use elementary and clear arguments to explain our main results. Finally, we proposed a new and unusual way to determine the type of laying of a graphene bilayer.