Theoretical Studies Of The Transport Properties In Graphene

Graphene is a new member in the carbon family and has been successfully fab-ricated in experiment several years ago. Due to its stability in room temperature and excellent transport property, it is possible for graphene to replace silicon as the main component of the next-generation semiconductor electronic device. Graphene has the linear dispersion at low energy and is different from the parabolic dispersion in tradi-tional semiconductor and has attracted a lot of interests in both theory and experiment. So it is of a great significance to study the electronic energy band and transport property of such a material. The dissertation is organized as follows:In chapter1, we will briefly introduce the electron property of graphene under the tight-binding approximation and summary the research progress in theory and exper-iment of the transport property in graphene system. We give a detailed illustration of method of calculation used in our dissertation:the transfer matrix method.In chapter2, we study the disorder and localization of electron in bilayer graphene. Under various kinds of disorder (site-energy disorder, in-plane hopping energy disorder, inter-plane hopping energy disorder), the electrons in bilayer graphene are localized, only when the case is zero energy and inter-plane hopping energy disorder, the system is extended and corresponds to certain conductivity, in accordance with the result of experiment.In chapter3, we consider the on-site Hubbard interaction in bilayer graphene and study the influence of disorder on the magnetism. With the help of mean-field theory, we find the diagonal disorder will not change the first-order property of the paramag-netism to ferromagnetism phase transition. But when the strength of disorder grows, the critical Hubbard interaction will increase.In chapter4, when the electric field exists, we consider the electric field as a pertur-bation to the system and get the evolution of conductivity in bilayer graphene with time. After a long time, the value of conductivity tends to a steady value, which fits well with data of the optical conductivity and the minimal conductivity measured experimentally. The physical explanation is that the electric field can excite the electron-hole pair. The coherent transport of the electron-hole pair leads to the oscillation of the conductivity.In chapter5, we study the Zitterbegung (ZB) effect in graphene systems. When a laser pulse acts on the graphene system, we can make use of the time-related per-turbation theory and get the observable quantity in experiment-electric field. After comparison, we find the ZB phenomena in graphene bilayer is easier to observe in experiment than in graphene monolayer.In chapter6, we study the influence of weak disorder on the quantum spin Hall state in HgTe/CdTe quantum well. It is found that there is minor effect of the weak disorder on the quantum spin Hall state. But near the critical point, disorder will enlarge the extension region.In chapter7, we use the Green’s function method in real space to study transport of the spin current in quantum wire where two perpendicular electric fields exist in different region. Our calculation suggests the charge current will be suppressed and the spin current can exhibit a larger value. This means such a setup is a good path to realize the spin current.