The Electronic Transport Properties In Graphene Nanostructure

The electronic transport properties in graphene nanostructureRecent experiments have discovered that graphene presents many unusual electronictransport properties, such as an anomalous half-integer quantum Hall e?ect, nonzero con-ductivity minimum at vanishing carrier concentration and subtle weak localization and soon. Electrons in the vicinity of the Dirac point exhibit a linear dispersion relation, a gap-less subband structure, and obey the massless relativistic Dirac equation, rather than theSchr¨odinger equation, therefore grapheme is the first two-dimensional material, which pro-vides a bridge between condensed matter physics and quantum electrodynamics, and opensnew perspectives for carbon-based electrons. Due to their high mobility at room temperatureand high concentrations of charge carriers, and the ease in the fabrication of graphene nanos-tructures, graphene can be considered as the base material of nanoelectrics. We thus thinkthat it is important to study the electron transport properties of various graphene nanos-tructures. In this thesis we report our theoretical investigations on the electronic transportproperties of several typical graphene nanostructures by means of the Dirac equation method,the tight-binding method, the generalized transfer matrix theory and the non-equilibriumGreen function technique.Graphene nanostructure presents many unusual electronic transport properties and soif we can find inner relation between the unusual electronic transport properties and an intrinsic property of Dirac fermion, which will provide some useful theoretical informationnecessary to realize electric nano-devices. Below we give a brief outline of our work.First, we pay attention to the electric state of two typical structures that consist ofarmchair and zigzag graphene nanoribbons. We not only obtain the electron eigen-statesanalytically but also Make the following observations . For the Armchair nanoribbon, thereis no relation between the transverse wave vector q and longitudinal wave vector kx due tothe quantum confinement. When the width is satisfy N = 3p + 2 with p being any integer,the nanoribbon is metallic. And the nanoribbons have duplicate degeneracy when the wavevector q = 0. If the width does not satisfy N = 3p + 2, then the semiconductor is non-degenerate and at the same time there are is no state with wave vector q = 0. For the Zigzagnanoribbon, the transverse wave vector q and longitudinal wave vector kx couple to eachother presenting surface states which are localized at the edge of the nanoribbon. We alsofound that the energy band are antisymmetric surround Dirac point. The calculated energyband structure agrees well with the results of tight binding method in the low energy regionif the nanoribbon size is not very small.Secondly, the linear conductance spectrum of a metallic graphene junction formed byinterconnecting two gapless graphene nanoribbons is calculated by the tight-binding method.We found that a strong conductance suppression appears in the vicinity of the Dirac point, al-though the match of the two linear subbands of the two metallic armchair graphene nanorib-bon provides an electron transmission mode. We found that such a conductance suppressionarises from the antiresonance e?ect associated with an edge state localized at the zigzag-edged shoulder of the junction. By analogy with T-shaped quantum dot structure we cangive a conclusion that the incident electron energy is aligned with the quantum-dot levels,the antiresonance is in fact a result of the destruction of quantum interference. Further- more, from the calculated spectra of the local density of states at some lattice points nearthe junction interface and comparing the structures of the shoulder junctions,we observedthat the center of the conductance valley, can be e?ciently displaced by applying a step-likepotential. Since the value in the Dirac point can be adjusted from 0 to 2e2/h, this featuresuggests that conductance suppression can be utilized to realize an electric nano-switch.Thirdly, we utilize study generalized transfer matrix theory to study electronic transportthrough graphene waveguide. In the e?ective mass approximation, electronic property ingraphene can be characterized by the relativistic Dirac equation. By using appropriatewavefunction boundary conditions at the junction interfaces, we generalize the conventionaltransfer matrix approach to formulate the linear conductance of the graphene waveguide interms of the structure parameters and the incident electron energy. In comparison with thetight-binding calculation, we find that this method is especially suitable to deal with thegraphene multiple junctions with relatively large sizes and having many junctions. In sucha case, it is much more timesaving to calculate the conductance spectrum by this methodthan performing a tight-binding calculation. The calculated results of conductance spectrumindicates that the graphene waveguide exhibits a well-defined insulating band around theDirac point, even though all the constituent ribbon segments are gapless. We attribute theoccurrence of the insulating band to the antiresonance e?ect which is intimately associatedwith the edge states localized at the shoulder regions of the junctions. We also employ thelanguage of Feynman path of the laterally coupled quantum dot chain to consider electroncorrelation. And to formulate the lateral quantum dot introduces new Feynman paths.As a result, the destructive quantum interference occurs among electron Feynman paths.Furthermore, such an insulating band can be sensitively shifted by a gate voltage, whichsuggests device application of the graphene waveguide as an electric nanoswitch. Finally, the contact conductance between graphene and two quantum wires which serveas the leads to connect graphene and electron reservoirs was theoretically studied by meansof non-equilibrium Green function technique. We also considered that there are many factorsthat in?uence the contact conductance, for example, the bandwidth and the band positionof the quantum wire(lead) relative to the Dirac point of graphene, the coupling configurationbetween the leads and graphene, and the distance and the relative orientation between thetwo leads, and so on. From the results of those in?uences on the contact conductance, wecan conclude that the contact conductance depends sensitively on the graphene-lead cou-pling configuration. When each quantum wire couples solely to one carbon atom, the contactconductance vanishes at the Dirac point if the two carbon atoms coupling to the two leadsbelong to the same sublattice of graphene. We find that such a feature arises from the chi-rality of the Dirac electron in graphene. If two quantum wires couple to two carbon atoms ofdistinct kinds, a resonant path can be formed by adjusting the strength of the graphene-leadcoupling. Such a chirality associated with conductance zero disappears when a quantum wirecouples to multiple carbon atoms. The general result irrelevant to the coupling configurationis that the contact conductance decays rapidly with the increase of the distance between thetwo leads. In the weak graphene-lead coupling limit, the carbon-carbon bond directions(i.e.τl directions) are the optimal directions to form the maximal contact conductance. In amore realistic situation, each quantum wire may couple e?ectively to multiple carbon atomsaround it. To mimic such a situation, we introduce Gaussian-type graphene-lead coupling,by which we worked out the two-dimensional conductance pattern formed by moving thesecond probe around the first one. We find that the conductance pattern does not varysensitively with the incident electron energy. However, the symmetry of the conductancepattern changes from C3 group to C6 group when the first probe shifts from a carbon atom to the center of a hexagon of the graphene lattice. Lastly, we obtained an approximativeexpression about the contact conductance when the probe interval is su?ciently large andthe incident electron energy is in the vicinity of the Dirac point. We found that in such acase the contact conductance is proportional to the square of the two contact areas betweengraphene and the probes, and inversely proportional to the square of the probe interval.