The Study Of Electronic Structure Of Circular Graphene Quantum Dot

Graphene is a two-dimensional material, which is one-atom-thick planar sheet of sp2-bonded carbon atoms that are densely packed in a honeycomb crystal lattice. The Nobel Prize in Physics for 2010 was awarded to Andre Geim and Konstantin Novoselov, who are physicists from the University of Manchester, for ground breaking experiments regarding the two-dimensional graphene. In the past few years, because of it's unique structure and many unusual intriguing physical properties, graphene has caused many researchers'extensive attention and is becoming the front research area in various relative fields.In this paper, electronic structures of graphene quantum dot with different boundaries have been simulated and calculated by solving a Dirac equation, which may provide some theoretical guidance for their applications in nano-electronic devices and novel sensors.In chapter 1, firstly, we give a brief introduction to the discovery of graphene and it's novel properties. Then we list some methods in producing graphene. At last, the potential applications of graphene in various relative fields have been described.In chapter 2, we introduce two fundamental theoretical model, lattice model and continuous model. Some of its properties are introduced, such as, band structure, effective mass and density of states. After that, a brief introduction of the numerical method used in this paper has been made, which lay the foundation for the following chapters.In chapter 3, the electronic structures of armchair graphene quantum dot in the presence of a perpendicular magnetic field have been studied by solving Dirac equation numerically. The energy spectrum has a gap which is inversely proportional to the radius of the graphene quantum dot in the absence of a magnetic field.As the magnetic field increases the Landau levels will appear and the degen- generacy of the Landau levels increase. The level spacing is inhomogeneous and declines quickly in the increase of state energy. The Landau-level energies are proportional to square root of Landau level index n and the magnetic field B simultaneously, which is coincide with the analytical results of graphene. The degeneracy of the lowest Landau level which is zero energy and independent of the magnetic field is proportion to the magnetic field and the square of radius of graphene quantum dot. We also find that, the density distribution will move from the edge to the center during the formation of the Landau levels.In chapter 4, we investigate the electronic structures of zigzag graphene quantum dot in the presence of a perpendicular magnetic field. We find that, while imposing the zigzag boundary, the degeneracy of valley will be broken by the magnetic field, that is K point and K'point are not symmetrical. The new zero energy states will emerge and the edge states will turn into the lowest landau level with the increase of magnetic field for K point. But it is very different for K'point. The new zero energy states can be tuned and the edge state do not change by the magnetic field.Conclusions and outlook are given in chapter 5.