Electronic band gap and transport in graphene superlattice with a Gaussian profile potential voltage

We study the electronic properties for the graphene-based one-dimensional superlattices, whose potential voltages vary according to the envelope of a Gaussian function. It is found that an unusual Dirac point exists and its location is exactly associated with a zero-averaged wave number (zero-k) gap. This zero-k gap is less sensitive to incident angle and lattice constants, properties opposing those of Bragg gap. The defect mode appearing inside the zero-k gap has an effect on transmission, conductance, and shot noise, which will be useful for further investigation.