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The effect of different stacking order of graphene multilayers on theelectric field induced band gap is investigated. We considered a positivelycharged top and a negatively charged back gate in order to independently tunethe band gap and the Fermi energy of three and four layer graphene systems. Atight-binding approach within a self-consistent Hartree approximation is usedto calculate the induced charges on the different graphene layers. We foundthat the gap for trilayer graphene with the ABC stacking is much larger thanthe corresponding gap for the ABA trilayer. Also we predict that for fourlayers of graphene the energy gap strongly depends on the choice of stacking,and we found that the gap for the different types of stacking is much larger ascompared to the case of Bernal stacking. Trigonal warping changes the size ofthe induced electronic gap by approximately 30% for intermediate and largevalues of the induced electron density.

Stacking Order dependent Electric Field tuning of the Band Gap in Graphene Multilayers