Electronic Transport In Graphene Under Modulated Magnetic Fields

Graphene presents many unusual electronic transport properties, such as an anoma-lous quantum Hall effect and Klein paradox and so on. Electrons in the vicinity of the Dirac point exhibit a linear dispersion relation, a gapless subband structure, and obey the massless relativistic Dirac equation, therefore graphene is the first two-dimensional material, which provides a bridge between condensed matter physics and quantum electrodynamics, and opens new perspectives for carbon-based electrons. Due to their high mobility at room temperature and high concentrations of charge carriers, and the ease in the fabrication of graphene nanostructures, graphene can be considered as the base material of nanoelectrics. We thus think that it is important to study the electron transport properties of graphene.In this thesis, we first introduce the physical properties and preparation of graphene, the geometry structure and recent progress on graphene. Then we introduce the theo-retical model and the research method. Lastly, based on the tight-binding model and Green function method, we systematically investigate the electronic transport proper-ties of graphene under a modulated magnetic field.Firstly, the effect of a modulated magnetic field on the electronic structure of neu-tral graphene is examined. It is found that application of a small staggered modulated magnetic field does not destroy the Dirac-cone structure of graphene and so preserves its fourfold zero-energy degeneracy. The original Dirac points are just shifted to other positions in k space. By varying the staggered field gradually, new Dirac points with exactly the same electron-hole crossing energy as that of the original Dirac points, are generated, and both the new and original Dirac points are moving continuously. Once two Dirac points are shifted to the same position, they annihilate each other and vanish. The process of generation and evolution of these Dirac points with the staggered field is found to have a very interesting pattern, which is examined carefully. Generally, there exists a corresponding branch of anisotropic massless fermions for each pair of Dirac points, resulting in that each Landau level is still fourfold degenerate except the zeroth LL which has a robust 4nt-fold degeneracy with nt the total number of pairs of Dirac points. As a result, the Hall conductivityσxy shows a step of size 4nte2/h across zero energy.Secondly, based on the tight-binding model, we study graphene under a one-dimensional modulated magnetic field which contains both a uniform and a staggered component. We find that graphene properties can be manipulated by a periodic po-tential. The chiral current-carrying edge states generated at the interfaces where the staggered component changes direction, lead to an unusual integer quantum Hall effect in graphene, which can be observed experimentally by a standard four-terminal Hall measurement. When Zeeman splitting is taken into account, a novel state is predicted where the electron edge currents with opposite spin polarization propagate in the op-posite directions at one sample boundary, whereas propagate in the same directions at the other sample boundary. Furthermore, all the interface edge currents are fully spin polarized with the same spin direction.Finally, electron fully spin-polarized edge states in graphene emerged at the inter-faces of a nonuniform magnetic field are studied numerically in a tight-binding model, with both the orbital and Zeeman-splitting effects of magnetic field considered. We show that the fully spin-polarized currents can be manipulated by a gate voltage. In order to make use of the fully spin-polarized currents in the spin related transport, a three-terminal experiment is designed and expected to export the fully spin-polarized currents.In summary, we systematically investigate the electronic transport properties of graphene under a modulated magnetic field, and obtain some interesting and useful re-sults. We expect these results can be observed in experiments and may have important application in electronic and spintronic devices.