A graphene-based superlattice formed by a periodic gap modulation is studied theoretically by using a Dirac-type Hamiltonian. Analyzing the dispersion relation, we have found that extra Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between the conduction and valence minibands disappears. The expressions for the positions of these Dirac points in k space and the threshold value of the potential for their emergence were obtained. Also, the dispersion law and renormalized group velocities around the extra Dirac points were calculated. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.
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Maksimova et al. (2012) studied this question.
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