The Study Of Electronic Structure Of Ring Graphene

Graphene is a single atomic layer of carbon atoms, whose structure is a two-dimensional honeycomb lattice. In2004, physicists from the university of manchester, Andre Geim and Konstantin Novoselov, who are isolated Graphene from graphite by mechanical removal methods in the lab for the first time. Due to it’s unique structure and many unusual intriguing physical properties. In the past few years,graphene which has caused many researchers’extensive attention is becoming the hotspot in fields of condensed matter physics.This paper is divided into five chapters.The first chapter is mainly a dis-cover, a unique electronic properties and test preparation of graphene. The second chapter we introduce two fundamental theoretical mode and some review of grapheme.After that, a brief introduction of the numerical method in this paper has been made. The third chapter we mainly introduce the properties of Dirac electron of low-dimensional disordered systems. The fourth chapter we mainly Study of electronic structure of zigzag graphene quantum ring problem.In chapter1, firstly, we give a brief introduction of the discovery of graphene, unique electronic structure and some novel transport properties such as anoma-lous quantum Hall effect and Klein tunneling effect,usually weak localizationIn chapter2,we primarily describes two basic theoretical model of single-layer Graphene and some of the results obtained by the model. Then introduce a simple method of numerical calculation, which lay the Foundation for the cal-culations below.In chapter3, we calculate the structure of energy spectrum and the electron density distribution of a Dirac electron in the present of a magnetic field and disorder by using the method of the finite difference. Then we discuss the effect of the different magnetic fields and disorder on the electron density distributions. With the increase of disorder strength, disorder gradually weakens the localiza-tion of the electron and makes the massless Dirac electron delocalized which is different from the Anderson localization theory.In chapter4,we studied on the Dirac equation and calculation the electronic structures of zigzag grapheme quantumn ring when it is loop in a magnetic field and discuss the Size effects on the structure of energy spectrum. We found that when there is no external magnetic field, energy spectrum structure zigzag grapheme quantunm ring in the presence of a perpendicular magnetic field for m and-m is Asymmetric.due to border States with zero energy system, the energy gap of the system is zero.When taking into account the magnetic field,The spectrum structure of K’ point changes, the new zero energy state of K’ point appears, The amount of the edge state and its density distribution do not vary with the magnetic field increases, still is a border State. The spectrum of graphene quantum ring under strong magnetic field appear of the Landau levels. The lowest Landau level energy is zero.Conclusion and outlook are given in chapter5.