The Research On Optics-like Transport Of Electrons In Graphene

Graphene, a new two-dimensional carbon material, has attracted much attentionfrom many scientists due to its particular physical properties since it wasexperimentally fabricated by the physicists from University of Manchester in2004.Differnent from the traditional semiconductor materials, the quasiparticles in singlelayer graphene are massless Dirac Fermions, which are governed by the masslessrelativistic Dirac equation. And the quasiparticles close to the Dirac point of theBrillouin zone possess a gapless linear energy spectrum. As a consequence, grapheneexhibits numerous unique electronic and transport properties, such as half-integerquantum Hall effect, special Andreev reflection，the minimal conductance, and Kleintunneling.In this thesis，we first study the properties of asymmetric graphene waveguideinduced by an asymmetric quantum well. We then investigate the transport propertiesof electrons tunneling through a graphene superlattice with periodic electrostaticpotentials. The main contents include the following aspects:First, we introduce zero-dimensional, one-dimensional, two-dimensional andthree-dimensional carbon materials. Then we introduce the preparation method,novel electronic properties and potential applications of graphene.Second, electrons in a graphene quantum well behave the quantum wave natureof electron, that is, electrons can refract, reflect, and interfere in a manner analogousto electromagnetic waves in a slab waveguide. Thus, an asymmetric quantum well ingraphene can act as a slab waveguide for electron waves. The conditions and thedispersion equation of guided modes in asymmetric waveguide are studied. Thereare three ways to generate guided modes in an asymmetric quantum wells ongraphene: i) Only Klein tunneling exists, ii) Only classical motion exists, iii) BothKlein tunneling and classical motion are present. In the case of (i) and (ii) in asymmetric graphene waveguide, the guided modes have similar characteristics withthat in symmetric waveguide. However, the case iii) only occur in the asymmetricgraphene waveguide.Third，the transmission coefficient of electrons tunneling through a graphenesuperlattice with periodic potential patterns has been deduced using the transfermatrix method. It is found that the transmission probability as a function ofincidence energy has more than one gap. The transmission gaps can be modulated bychanging the period number, the incidence angle, the height and width of thepotential. The positions of transmission gaps are independent with the period number,but more transmission gaps can be obtained by increasing the period number. Theincrease of barrier height of and well width will also result in more transmissiongaps. Moreover, the width of transmission gap increases with the incidence angleand barrier height, while reduces with the well width.Fourth, the transmission probability of electrons tunneling through a graphenesuperlattice with periodic potential patterns has been deduced. It is found that thereare two resonance conditions for the graphene superlattices. Some of the resonancetransmission peaks present N-1resonance splitting for electrons tunneling through Nbarrier. However, there is no explicit splitting rule for the conductance and shot noise.The resonance splitting effect depends on the incidence angle while the height andwidth of the potential has an impact on the number of resonant transmission peaks.Furthermore, the resonant splitting rule of the transmission is not sensitive on theshape of the potential barrier.