  The electronic structure of a single-layer graphene with a periodic Fermi
velocity modulation is investigated by using an effective Dirac-like
Hamiltonian. In a gapless graphene or in a graphene with a constant energy gap
the modulation of the Fermi velocity, as expected, only changes the dispersion
between energy and moment, turning the minibands narrower or less narrow than
in the usual graphene depending on how the Fermi velocity is modulated and the
energy gap remains the same. However, with a modulated energy gap it is
possible to control the energy gap of graphene by Fermi velocity engineering.
This is based on a very simple idea that has never been reported so far. The
results obtained here reveal a new way of controlling the energy gap of
graphene, which can be used in the fabrication of graphene-based devices.
