Dissertation
Dissertation > Mathematical sciences and chemical > Chemistry > Inorganic Chemistry > Non-metallic elements and their compounds > Part Ⅳ family of non-metallic elements (carbon and silicon ) and its compounds > Carbon C

The Property of Electron and Electron Transport in Graphene

Author YuanJianHui
Tutor ChengZe
School Huazhong University of Science and Technology
Course Optics
Keywords Graphene tight-binding approximation electronic states relativisiticwave equation quantum transport magnetic potential waveguide
CLC O613.71
Type PhD thesis
Year 2012
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Graphene, which is a single two-dimensional array of carbon atoms with a honeycomb lattice, has recently attracted intensive attention for its discovery in 2004 year because its charge carriers are massless, relativistic particles. The presence of such Dirac-like quasiparticles can be controlled by external field or size of sample or lattice topology, which is expected to induce some unusual electronic properties which make much difference from the two dimensional electronic gas, such as so-called Klein paradox, the anomalous integer quantum Hall effect, observation of minimum conductivity and so on. In room temperature, the electron with high edge mobility, so graphene is likely to replace silicon materials and cause a information communication technology revolution. Thus, to study the property of electron in graphene is with high theoretical and practical application value. In this thesis, we use super-cell theory, Dirac equation, the transfer matrix and scattering theory to investigate the property of electron and electron transport in graphene, which can provide theoretical guidance for their applications in nano-electronic devices and electronic fiber.The research content is divided into the following five parts:(1) The first part is the introduction part, which introduces the development process of carbon materials, the background of graphene and the methods of prepa-ration. In this chapter, we introduce the current research status of graphene and its application value.(2)In chapter two, we give a detailed introduction about the structure of graphene and the property of the electron in it.(3)In chapter three, using tight-binding approach to build the Harper’s equation and dirac equation, we investigate the property of electron in graphene nanoribbon in the absence(presence) of magnetic field. We find that the electronic properties of a nanometer scale carbon system depend strongly on its size and geometry showing the quantum size effect. For the zigzag graphene ribbon, a edge state will appear near the zero energy, which mainly steps from the confinement of the structure of edge to the site of carbon atoms. For the armchair graphene ribbon, we can see that there exists a change from insulating state to metallic state by changing the width of ribbons. In the presence of magnetic field, Landau level appears in the energy band, but when the magnetic field is very strong, landau level forms some subbands with cosine.(4) In chapter four, we mainly aim to discuss the unusual phenomena—the min-imum of conductivity. We investigate the property of electronic transport of armchair graphene ribbon takeing two different confinement of edge into account. We find that this conductivity can be changed in relation to the change of the gated voltage、bias voltage and magnetic field. We can see that a small bias voltage can induce a cur-rent, which indicates a nonzero minimum conductivity related to a maximum of Fano factor. We can find that a little increase of conductivity as the increase of the barrier voltage, but no obvious change for the ballistic graphene. In the presence of magnetic field, we can find that the magnetic effect is very obvious, and it can suppress the shot noise. For all of these factors, the conductivity always show a quantum oscillations with change the voltage or magnetic field in a finite width of graphene nanoribbon. For ballistic graphene, no oscillation occurs with changing voltage. The phenomena of quantum oscillations maybe relate to some localized quantum states lying near in the Fermi energy.(5) In chapter five, we study in the absence or presence of magnetic field Dirac fermion transport through a model of velocity barriers. The dirac electron in graphene penetrating into a velocity barrier is similar to photons through a different medium. We designed a way to construct a two-dimensional Dirac electron gas in graphene heterojunction by doping. We calculate the angular-dependent trans-mission probability to investigate the effect of resonant tunneling and magnetically induced wave vector filtering. We find confined state can close the ballistic channel causing resonant tunnelling peaks decrease. Moreover, We find strong wave vector filtering and resonant effect. These interesting features will be more helpful for developing new type of devices, such as wave vector filtering, magnetic control switches and so on. Finally, we investigate the guide modes in graphene confining by a velocity barrier. the bound states can serve as waveguide in graphene. We can see that the fundament mode always exist but the high-mode may disappear by changing the ratio of velocity. These discrete guided modes imply that there is a lowest cutoff frequency for an incident electron and that the incident electrons with different angles may have different minimum cutoff frequencies. These interesting features will be helpful for the investigation on an electronic fiber.

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