Abstract
It is known that a perpendicular electric field applied to multilayers
of graphene modifies the electronic structure near the K point and may
induce an energy gap in the electronic spectrum which is tunable by the
gate voltage. Here we consider a system of graphene multilayers in the
presence of a positively charged top and a negatively charged back gate
to control independently the density of electrons on the graphene layers
and the Fermi energy of the system. The band structure of three- and
four-layer graphene systems in the presence of the top and back gates is
obtained using a tight-binding approach. A self-consistent Hartree
approximation is used to calculate the induced charges on the different
graphene layers. We predict that for opposite and equal charges on the
top and bottom layers an energy gap is opened at the Fermi level. For an
even number of layers this gap is larger than in the case of an odd
number of graphene layers. We find that the circular asymmetry of the
spectrum, which is a consequence of the trigonal warping, changes the
size of the induced electronic gap, even when the total density of the
induced electrons on the graphene layers is low.
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