Electronic structure of a two-dimensional graphene monolayer in a spatially modulated magnetic field: Peierls tight-binding model

Magnetoelectronic properties of a two-dimensional (2D) monolayer graphene are investigated by the Peierls tight-binding model. They are dominated by the period, strength, and direction of a spatially modulated magnetic field. Such a field could induce the reduction in dimensionality, change of energy dispersions, anisotropy at low energy, composite behavior in state degeneracy, extra band-edge states, and asymmetry of energy bands. There are partial flatbands at the Fermi level and one-dimensional parabolic bands at others. These make density of states exhibit delta-function-like structure and asymmetric prominent peaks, respectively. Energies of the extra band-edge states strongly depend on the period, while those of the original band-edge states exhibit little dependence. Both of them grow as the strength increases. The modulated and uniform magnetic fields differ from each other in energy dispersion, state degeneracy, and dimensionality. Important differences between a monolayer graphene and a 2D electron gas also exist.