▎ 摘　　要

We propose a tunable electronic band gap and zero-energy modes in periodic heterosubstrate-induced graphene superlattices. Interestingly, there is an approximate linear relation between the band gap and the proportion of an inhomogeneous substrate (i.e., percentages of different components) in the proposed superlattice, and the effect of structural disorder on the relation is discussed. In an inhomogeneous substrate with equal widths, zero-energy states emerge in the form of Dirac points by using asymmetric potentials, and the positions of Dirac points are addressed analytically. Further, the Dirac point exists at k = 0 only for specific potentials; every time it appears, the group velocity vanishes in the k(y) direction, and the resonance occurs. For general cases of an inhomogeneous substrate with unequal widths, part of the zero-energy states are described analytically, and differently, they are not always Dirac points. Our prediction may be realized on a heterosubstrate such as SiO2/BN.