Proof for the electronic band crossing in sliding bilayer graphene

Dirac points are found to emerge due to the crossing of bands in the electronic structure of so-called sliding bilayer graphene. Group representation theory analysis corroborated with a tight-binding model for the ${p}_{z}$ orbitals is employed to demonstrate that the band crossings of energy dispersion curves at generic $\mathbf{k}$ points are guaranteed by the compatibility relations between the symmetries of eigenstates at the high-symmetry $\mathbf{k}$ points in the Brillouin zone. The Lifshitz transition picture and the transport properties of the systems are shown as consequences of the presence of Dirac points in governing the geometrical and topological properties of the Fermi energy surfaces.