Spin Or Valley Polarized Electron Transport Properties In Graphene

Graphene, an atomically thin layer of graphite, is the first discovered trulytwo-dimensional crystal material. Because of its peculiar lattice structure andelectronic properties, it has brought great interest in the scientific community.Graphene is a gapless semiconductor: the valence and conduction bands toucheach other at K and K’ points, i.e., the two inequivalent corners of the hexagonalBrillouin zone. Both of them have linear dispersion relationship around zeroenergy, so the low-energy electron or hole around either of them can be describedby the massless Dirac equation. Thus, K and K’ points are named as Dirac points.As a result, we call the Dirac-cone-like band structure formed in the vicinity ofthe two Dirac points, K and K’ valleys, respectively. In fact, the electronic wavefunction in K or K’ valley is a two component spinor, which describes the twodistinct sublattices of graphene. This implies that in graphene the low-energyelectron or hole near the Dirac points possesses two more degrees of freedom, thevalley and pseudospin degrees of freedom. The former refers to the twoinequivalent band valleys. And the latter stems actually from the bipartitesublattices. In this thesis, we investigate the feasibility of the spin or valleypolarized electron transport in graphene theoretically, and propose the physicalmodel to manipulate the electron spin or valley degree of freedom.In Chapter one, we give an outline of the development and application ofcarbon-nanotube-based and graphene-based nano electronic devices.In Chapter two, we introduce the lattice structure and electronic properties ofgraphene, in addition, the relevant theoretical methods, such as the tight-bindingmodel, Landauer-Büttiker formula and first-principles calculation method, arealso briefly presented. In Chapter three, the electronic transmission spectrum of a graphenenanojunction formed by interconnecting two armchair-edged graphenenanoribbons is obtained from the first principle calculation. We find that in such astructure the electronic transmission is remarkably spin-polarized near the Diracpoint. In fact, the origin of the spin-polarization is the antiresonance effect,generated from the edge state localized at the zigzag-edged shoulder of thenanojunction. When the size of graphene nanojunction gets larger, thespin-polarization becomes more remarkable. But the localized edge states cannotsurvive if the size of zigzag edge is smaller than that displayed by six carbonatoms. We account for this spin-polarized phenomenon reasonably byantiresonance effect.In Chapter four, we investigate the electronic and transport properties of anextended line defect in pristine graphene by means of tight-binding approach aswell as first-principles calculation method. Firstly, we have obtained the analyticalsolutions of quasi-one-dimensional boundary states around the extended linedefect embedded in a graphene lattice. We find that the odd-parity boundary stateswith respect to the line defect show a flat dispersion spanning two inequivalentvalleys. The wavefunctions of these states on one side of the line defect justcoincide with the edge state localized at the zigzag edge of a semi-infinite pristinegraphene sheet. More interestingly, the line defect can also induce even-parityboundary states (EPBSs) which are absent at a zigzag edge. These EPBSs formsubband segments which appear around the Dirac point, the top and the bottom ofthe total π-band. In particular, one of the EPBS subbands with nontrivialdispersion persists in the bandgap of the bulk band if it is gapped. Such a subbandprovides a one-dimensional channel to carry the current flowing along the linedefect, which is robust to intravalley scattering. Secondly, we have theoreticallyinvestigated the energy band structure and the electronic transport properties of aone-dimensional superlattice formed by patterning graphene lattice with a periodic line defect array (hereafter such a superlattice is abbreviated to LDGSL).We find that the anisotropy of the Dirac cone has a nontrivial influence on theuniversal minimum conductivity and the sub-Poissonian shot noise. Lastly, wepropose a valley polarized electronic transport structure. This structure consists ofa finite-length LDGSL, sandwiched between two pieces of semi-infinite pristinegraphene. The calculated electronic transmission spectrum of such a structureshows the nearly perfect valley polarization for low-energy incident electrons.In Chapter five, we demonstrate that valley-filtering switch can be realized ina carbon nanotube (CNT) embedded with a series of Stone-Wales defects(SWCNT). This structure consists of a finite segment of the SWCNT connected totwo semi-infinite pristine CNTs which serve as the two leads. In this device, thevalley polarization is close to100%. In addition, by a further numericalcalculation we also find that the valley valve function can be realized by tuningthe gate voltage appropriately. Then we study the influence of the practicalscatterers on the valley-filtering effect. The results demonstrate that thevalley-filtering effect persists even though the disorder scattering is drasticallystrong. In contrast, the vacancies can damage the valley-filtering effect morenotably. However, the valley filtering effect still remains when vacancyconcentration is restricted less than1.0%. These results demonstrate that this kindof CNT is a feasible device prototype for valleytronics application.In Chapter six, we have investigated the interaction between the intrinsicedge state of graphene and the helical boundary state of topological insulator (TI)phase in bilayer graphene within the tight-binding model. It is found that in azigzag-edged nanoribbon of bilayer graphene, due to the interaction between theseedge states, it is possible that the TI helical state does not localize at the TI phaseboundary. Instead it moves to nanoribbon edge though the spin-orbital coupling isabsent therein. Moreover, the helical edge states at the opposite sides of the TI phase have the same, rather than the opposite helicity as the usual case. And thehelicity of these edge states is converted as the eigen-energy shifts across theDirac point. When we introduce the line defects to induce the intrinsic boundarystate of graphene, we find that the gapless mode numbers in the bulk bandgap atthe two line defects are not equal to each other. Such a symmetry breakdown alsoresults from the hybridization between the TI and line defect boundary states.However, it contradicts the bulk-edge correspondence of the Z2TI.