Graphene superlattice with periodically modulated Dirac gap

Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the position of these Dirac points in $\mathbf{k}$-space and threshold value of the potential for their emergence were obtained. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.