Influence of modulated fields on the Landau level properties of graphene

Abstract

The influences of modulated electric fields and modulated magnetic fields on low-energy Landau levels (LL's) of monolayer graphene are investigated by the tight-binding model. The ratio of the uniform magnetic-field strength to the modulated field strength is arbitrarily chosen for discussions. Both modulated fields cause the LL's to split into two twofold parabolic subbands; these subbands exhibit periodic oscillations and two kinds of band-edge states. However, the subband dispersions and oscillation amplitudes associated with electric and magnetic modulated fields behave differently. The main features of the electronic structure are reflected in the density of states, which presents pairlike and square-root divergent structures for both modulated field cases. The LL wave functions are strongly affected by both modulated fields, such as the broken symmetry, displacement of the center location, and alteration of the amplitude strength. These changes in the LL wave functions should be reflected in other physical properties, e.g., the optical selection rules. Furthermore, the dependence of the LL properties on the modulation strength and modulation period is also discussed in detail.