Quantum Transport In Graphene And Topological Insulators Junctions

Graphene and topological insulators are hot materials for the research in condensed matter physics in the past several years. Compared with traditional materials, the most distinguished characteristic in these two kinds of materials is that, the energy dispersion of the electrons near Fermi level is linear, and the electrons are described by the relativis-tic Dirac equation. In contrast, the dispersion of electrons at low energy in the traditional condensed materials is parabolic, and the electrons are described by the nonrelativistic Schrodinger equation. Thus graphene and topological insulators are called Dirac ma-terials. These Dirac materials have opened the fields of "relativistic" condensed matter physics.We study the quantum transport in the various heterostructures composed of graphene or topological insulators in proximity to ferromagnets or superconduc-tors, including the ferromagnetic graphene junction, the graphene-based ferromag-net/insulator/superconductor junction, the ferromagnetic zigzag graphene nanoribbon Josephson junction, and the superconductor/two-dimensional ferromagnetic topological insulator/superconductor junction. In these heterostructures, the emerged Dirac Fermions exhibit many peculiar transport properties which are quite different from that in the het-erostructures made up of the traditional materials. In detail, the dissertation is organized as follows:In chapter one, we give a brief introduction to graphene and topological insulators, mainly referring to their basic physical properties. Then we describe two theoretical meth- ods, scattering theory and Green's function method, which we have used to study this two kinds of materials.In chapter two, we study the tunnel magnetoresistance (TMR) and spin transport in ferromagnetic graphene junctions composed of normal graphene (NG) and ferromag-netic graphene (FG) layers. We find that the TMR in the FG/NG/FG junction oscillates from positive to negative value with respect to the chemical potential controlled by a gate voltage in the central barrier region, as the Fermi level locates below one of the Dirac points of the two spin subbands in the FG. More interesting, the conventionally defined TMR in the FG/FG/FG junction oscillates periodically from the positive to the negative as the barrier potential increases in spite of Fermi energy in the FG electrodes. The spin polarization of the current through the full ferromagnetic graphene junction also has an oscillating behavior with changing the gate voltage, whose oscillating amplitude can be modulated by the exchange energy in the ferromagnetic graphene.In chapter three, we study the electronic transport in a graphene-based ferromagnet/insulator/d-wave superconductor junction by using the the Dirac-Bogoliubov-de Gennes equation. We take into account the effects of spin polarization in the ferromagnetic graphene, barrier strength in the central region, and Fermi wave vector mismatch between the ferromagnetic and superconductive regions. We find that the differ-ential conductance and shot noise are remarkably modulated by these parameters, which is distinctly different from that in other junctions. The most interesting finding is that, the conductance, shot noise and Fano factor in our system are completely determined by one parameter, i.e. the spin polarization, irrespective of all the other parameters, as the bias voltage in the junction approaches zero and the orientation angle of the superconductive gap relative to the longitudinal direction of the junction maximizes. This universal trans-port properties could be used to measure the spin polarization of ferromagnetic graphene and identify the specular Andreev reflection in experiments.In chapter four, we study the supercurrent through a superconductor/ferromagnetic zigzag graphene nanoribbon/superconductor junction by means of the Matsubara Green's function method. We find that the direction of supercurrent through the Josephson junc-tion can be reversed by inducing a uniaxial strain in the graphene nanoribbon. It is found that such strain-induced0-π transition results from the dependance of the effective Fermi velocity on uniaxial strain in graphene nanoribbon controlled by mechanical approaches. Furthermore, we find that the switch of the Josephson junction between the0and π states is remarkably modulated by the combination of the uniaxial strain and the gate-controlled barrier potential.In chapter five, we study the Josephson effect in an s-wave superconductor/two-dimensional ferromagnetic topological insulator/s-wave superconductor junction by use of the Matsubara Green's function method. We find that the direction of the edge su-percurrents through the Josephson junction can reverse, i.e.,0-π transition occurs, as the exchange field breaks both of the time reversal symmetry and sublattice symmetry in the magnetically doped topological insulator. The unconventional0and π states are pro-tected by the topological properties of the quantum spin Hall state in the two-dimensional ferromagnetic topological insulator, so that they are insensitive to weak disorder. More interesting, as the superconducting phase difference between the two superconductors is0or π, the edge supercurrents become chiral, i.e., the total supercurrents through the Josephson junction is zero, but the finite equal edge currents at the opposite edges flow in the opposite directions.In the last chapter, we make a summary and give some outlook for the future inves-tigation.