Electronic properties of monolayer graphene in the presence of the uniform magnetic and modulated electric fields

The influence of modulated electric fields on low-energy Landau levels (LLs) of single-layer graphene is investigated by the Peierls tight-binding model. Such fields strongly affect the electronic properties of LLs, i.e., they split the LLs into the parabolic bands, produce the extra band-edge states, break the state degeneracy, and increase the dimensionality. The extra band-edge states make the density of states (DOS) exhibits many pairs constructed by the two square-root divergent peaks. The energy spacing between the pair peaks is proportional to the electric field strength (V0), and the peak intensity displays an inverse proportion to V0. However, DOS is independent of the modulated period. Furthermore, the dependence of the peak frequency on the electric field strength is also discussed in detail. The predicted results could be verified by the experimental measurements.