Disorder Effects On Electronic Tructure And Quantum Transport Properties In Graphene Systems

Graphene was first discovered in laboratory in2004. Graphene is a two-dimensional (2D) system that has attracted much attention in recent years because of its perfect electronic properties. From the view of scientific research, owing to the linear dispersion near the vicinity of the two inequivalent corners K and K’ of the first Brillouin zone, the electrons in undoped graphene are governed by the relativistic massless Dirac equation, as opposed to the usual Schrodinger equations for2D electrons in solids. From the view of application, graphene has very high electron mobility so that it is promising in next-generation high-speed electric circuit. Thus, it is important to study the graphene from the viewpoint of basic scientific research and applications.In the first chapter of my thesis, I will give a brief introduction about the discovery of graphene and the application of graphene. Then I will show how to obtain the massless Dirac equation in graphene from the tight-binding hamil-tonian. I will emphasis on discussion how the various type of disorder affect electronic structure and quantum transport properties in graphene.In the second chapter of the thesis, we study the effects of the non-resonant scattering (e.g. short-ranged impurities) and resonant scattering (e.g. vacancies, adatoms) on electronic structure and quantum transport properties in graphene in the absence of magnetic field. In the case of non-resonant scattering, we calculate the spectral function and related self-energy function. The fundamental physical quantities like the elastic relaxation time Te, the phase velocity vp, and the group velocity vg are evaluated. New features around the Dirac point are revealed, indicating that hybridization of Bloch states plays an important role in the vicinity of the Dirac point. In the case of resonant scattering, it is found that each Dirac nodal point splits into two new nodal points due to the coherent multiple scattering among vacancies. The energy split between the two nodal points is proportional to the square root of vacancy concentration. In addition, an extra dispersionless band is developed at zero energy. Our theoretical prediction offers an excellent explanation to the recent experiments.In the third chapter of the thesis, we study the disorder effects on electronic structure and quantum transport properties in graphene in the presence of high magnetic field. We calculate the density of states (DOS) of graphene and we find that the disorder-broadened zero-energy Landau subband has a Gaussian shape and its width is proportional to the random potential variance and the square root of magnetic field. Moreover, we introduce a interpretation to the sizeable shift of Cyclotron Resonance experiment based on the disorder-induced shift of Landau subband. We also provide a physical picture to understand the observed field-driven metal-to-insulator transition at filling factor v=0based on the competition between Peierls lattice distortion and intrinsic ripples.