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Dirac points are found to emerge due to the crossing of bands in theelectronic structure of bilayer graphene for configurations in which thealignment between two hexagonal lattices preserves the parallelism of thearmchair/zigzag lines between two layers. On the base of electroniccalculations using a tight-binding model for the $\pi$ bands it is shown thatthe crossing of the energy-band dispersion curves occurs in the vicinity of thecorner points of the hexagonal Brillouin zone. Group representation theoryanalysis confirms the emergence of such Dirac points. It is demonstrated thatthe band crossings at generic $\mathbf{k}$ points are guaranteed by thecompatibility relations between the symmetries of eigenstates at thehigh-symmetry $\mathbf{k}$ points in the Brillouin zone. The presence of Diracpoints governs the geometrical properties of the energy surfaces, and thus thetopological structure of the Fermi energy surface and the energy spectrum.

Electronic band crossing in sliding bilayer graphene: Tight-binding calculations and symmetry group representation analysis