Tunneling Properties Of Dirac Electrons On The Strained Graphene Driven By The Magnetic Fields

The graphene, a single-layer two-dimensional carbon materials, has been recently subjected to the intensive research due to its salient electronic and optical properties, such as, anomalous quantum Hall effect, Klein tunneling, specular Andreev reflection, and minimal conductivity, etc. The Dirac particles in the graphene obey the massless Dirac equations, which can be obtained through the Taylor expansion around the special point K(K’) in the Brillioun zone in the framework of the tight-binding approximation. The graphene sheets are usually grown on the insulating substrate, such as, silica, or alumina, etc, which results in the stress (strain) due to the lattice mismatch. In this thesis, the strain is taken into account by employing the anisotropic Dirac equation instead of the isotropic one with the Fermi velocity about 1/300 of the light. Our thesis is mainly divided into two parts:(1) The first part investigates the transport properties of the Dirac particle in the pristine graphene under the influence of the periodic linear electric potentials. The transmission, conductance and electric currents flowing through the multiple periodic linear electric potentials barriers have been obtained using the piecewise transfer matrices, which can be used in the nonsingular as well as singular cases due to the intractable infinite matrix elements. The corresponding superlattices are also studied, where the minibands and density of states are numerically given and analyzed. It is found that the period of the unit cells plays a profound role in both the miniband profiles and density of states, such as energy gaps, the band shape around the intersections between the conduction and valence bands, and humps within the curves of the density of states.(2) The effects of the strain on the two kinds of multiple quantum wells with magnetic barriers, one is composed of the strained strip in the positive magnetic field on the left side, and the pristine strip in the negative magnetic field on the right side are investigated, which is modeled by the anisotropic massless Dirac equation. The transmission, the conductance for the quantum wells and the corresponding energy bands are investigated and interpreted. It is found that the strain favors both the transmission and conductance of the Dirac particles. The energy band profiles from the two different configurations show the striking differences due to the different degree of strains. Furthermore, the transmission, conductance and the corresponding energy bands shows the striking differences between the electric scalar potentials and magnetic vector potentials.