Electronic structure of a monolayer graphite layer in a modulated electric field

The π-electronic structure of a monolayer graphite, with or without a uniform magnetic field, is studied by the tight-binding model. Electronic properties strongly depend on the strength, the direction, and the period of the modulated electric field. Such field could lead to the drastic changes in state degeneracy, energy dispersions, band spacings, wave functions, and band-edge states. The main features of energy bands are directly reflected in density of states. DOS could exhibit special structures, such as asymmetric square-root divergences, symmetric logarithmic divergences, symmetric delta-function-like divergences, and discontinuities.