  The effect of different stacking order of graphene multilayers on the
electric field induced band gap is investigated. We considered a positively
charged top and a negatively charged back gate in order to independently tune
the band gap and the Fermi energy of three and four layer graphene systems. A
tight-binding approach within a self-consistent Hartree approximation is used
to calculate the induced charges on the different graphene layers. We found
that the gap for trilayer graphene with the ABC stacking is much larger than
the corresponding gap for the ABA trilayer. Also we predict that for four
layers 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 as
compared to the case of Bernal stacking. Trigonal warping changes the size of
the induced electronic gap by approximately 30% for intermediate and large
values of the induced electron density.
