  In this paper, we investigated the effects of periodic external potentials on
properties of charge carriers in graphene using both the first-principles
method based on density functional theory (DFT) and a theoretical approach
based on a generalized effective spinor Hamiltonian. DFT calculations were done
in a modified Kohn-Sham procedure that includes effects of the periodic
external potential. Unexpected energy band gap opening and quenching were
predicted for the graphene superlattice with two symmetrical sublattices and
those with two unsymmetrical sublattices, respectively. Theoretical analysis
based on the spinor Hamiltonian showed that the correlations between
pseudospins of Dirac fermions in graphene and the applied external potential,
and the potential-induced intervalley scattering, play important roles in
energy-gap opening and quenching.
