Tunable band gap in graphene with a noncentrosymmetric superlattice potential

We show that, if graphene is subjected to the potential from an external superlattice, a band gap develops at the Dirac point provided the superlattice potential has broken inversion symmetry. As numerical example, we calculate the band structure of graphene in the presence of an external potential due to periodically patterned gates arranged in a triangular graphene superlattice (TGS) or a square graphene superlattice with broken inversion symmetry, and find that a band gap is created at the original and, in the case of a TGS, the second generation Dirac point. This gap, which extends throughout the superlattice Brillouin zone, can be controlled, in principle, by changing the external potential and the lattice constant of the superlattice. For a square superlattice of lattice-constant 10 nm, we have obtained a gap as large as 65 meV, for gate voltages no larger than 1.5 V.