Theoretical Study Of Electron Transport Properties And The Topological Properties In2-Dimensional Single Layer Graphene

Since its first discovery, graphene has attracted tremendous and long attention as a two-dimensional carbon material. Because of the unique properties of its band structure, graphene has been seen as the hallmark of the future semiconductor industrial. The main difference between graphene and traditional semiconductors is the appearance of Dirac cone near the fermi energy, hence graphene has also been called Dirac material. The researches around graphene generate a new field in condense-matter-physics.We theoretically investigate the transport properties of graphene in different circum-stances, including Rashba Spin-orbit coupling, topological gap, staggered potential and coulomb interaction. We find that graphene exhibit many unusual features under different circumstances, and one can build graphene devices using according physical mode. The dissertation is organized as follows:In chapter one, we give a brief introduction about the basic properties of graphen, such as the band structure of bulk graphene and graphene nanoribbons, the topological properties of gapped graphene. And we describe several theoretical methods which are very useful for calculate the transport properties of particular graphene devices.In chapter two, we use the tight-bonding approximation to calculate the band struc-tures of several two-dimensional carbon allotropes. And we find three two-dimensional carbon material which exhibit Dirac cone in their band structures other than graphene. Most importantly, we give all the analytical expression of the energy dispersion relation-ship in the vicinity of the Dirac cones. In chapter three, by using non-equilibrium Green’s function method and Landauer-Biittiker formula, we calculate the conductance of a graphene zigzag-nanoribbon het-erostructure modulated by Rashba spin-orbit coupling. We find that graphene nanoribbon also has the behavior of the Datta-Das field transistor and at the same time a giant magne-toresistance effect can be observed. Moreover, the same heterostructure can also be used as a conductance switch. Our findings show the potential of graphene nanostructure in the future semiconductor industry.In chapter four, using the mean-field approximation of the Hubbard model, we inves-tigate the topological phase transition of the graphene system with a intrinsic spin-orbit coupling undergoing a coexistence of a Coulomb interaction and a staggered potential. We find a new topological class in the graphene system which has Chern number1and spin Chern number1/2. We confirm our conclusion by counting the number of the edge states of graphene nanoribbons belong to different topological classes.In chapter five, we use Rashba spin-orbit coupling and staggered potential build a device which can generate pure valley current in graphene system. Valley index as a extra dimension will carry information as the spin index, and has huge potential.In chapter six, we summarize our researches and give some suggestions for future investigation.