Magneto-electronic properties of graphene nanoribbons in the spatially modulated electric field

The Peierls tight-binding model with the nearest-neighbor interactions is used to calculate the magneto-electronic structure of graphene nanoribbons under a spatially modulated electric field along the y  -axis. A uniform perpendicular magnetic field could make energy dispersions change into the quasi-Landau levels. Such levels are composed of the dispersionless and parabolic energy bands. A spatially modulated electric field would further induce a lot of oscillating parabolic bands with several band-edge states. It drastically modifies energy dispersions, alters subband spacings, destroys symmetry of energy spectrum about kx=0kx=0, and changes features of band-edge states (number and energy). The above-mentioned magneto-electronic structures are directly reflected in density of states (DOS). The modulation effect changes shape, number, positions, and intensities of peaks in DOS. The predicted result could be tested by the optical measurements.