Abstract We investigate the effect of asymmetry in bilayer graphene induced by a diatomic substrate (such as SiC) and its influence on the bilayer spectrum in zero and strong magnetic fields. We also determine selection rules for inter-Landau level transitions, taking into account all four π bands. The discovery of self-standing graphene-planes of carbon atoms arranged in a honeycomb lattice [1]-stimulated intense studies of monolayer and bilayer graphene structures (see Also, interest in optical properties of graphene resulted in several experimental magneto-optics studies of graphene in FIR, IR and the visible range In this paper, we investigate the combined effect of intralayer and interlayer asymmetries caused by a substrate on the electronic spectra of bilayer graphene, both with and without applied magnetic field. We show that intralayer asymmetry leads to the opening of an indirect gap with a 'Mexican hat'-type feature in one of the bands (whether conduction or valence depends on the sign of the asymmetry) and to an asymmetric density of states (DOS). This is different to the DOS in 'biased' bilayer graphene A schematic view of bilayer graphene (marked with the hopping integrals considered throughout this paper) and the Brillouin zone of bilayer graphene are shown in , 0) (where ξ ∈ {+, −} and a is the lattice constant). We restrict ourselves to nearest neighbour inplane and A1(2) ↔ B2(1) interactions in the tight-binding approximation of π orbitals ψ μi (μ ∈ {A, B}, i ∈ {1, 2}) and parametrize hopping integrals and on-site asymmetries according to the Slonczewski-Weiss-McClure mode
