Trilayer graphene nanoribbon carrier statistics in degenerate and non degenerate limits

We present trilayer graphene nanoribbon carrier statistics in the degenerate and the nondegenerate limits. Within zero to 3kBT from the conduction or valence band edgers high concentrations of carriers sensitively depend on a normalized Fermi energy which is independent of temperature. The effect of different stacking orders of graphene multilayers on the electric field induced band gap is studied. The gap for trilayer graphene with the ABC stacking is much larger than the corresponding gap for the ABA trilayer. The gap for the different types of stacking is much larger as compared to the case of Bernal stacking. A non-monotonic dependence of the true energy gap in trilayer graphene on the charge density is investigated along with the electronic low-energy band structure of ABC stacked multilayer graphene. The band structure of trilayer graphene systems in the presence of a perpendicular electric field is obtained using a tight-binding approach