Semimetallic graphene in a modulated electric potential

The pi-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the modulation period and potential strength. Such a potential could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. One striking feature happens close to the Fermi level that the light-cone structure is replaced with two distinct kinds of valley structures with highly anisotropic energy dispersion. Both valleys are highlighted by the existence of the quasi-one-dimensional electronic states, whereas they are distinguished one from the other by the different directions of restricted motion of charge carriers. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states.