Electronic and transport properties in carbon nanostructures

This dissertation studies the electronic and transport properties in one and two dimensional carbon systems, including carbon nanotubes, carbon chains and graphene. The focus is on the e ects of e-e interaction on these properties. First we studied the electron band structure of armchair CNTs under interaction. The interactions destroy the metallic ground states in the non interacting picture and open a gap in the electron energy spectrum. The e-e interaction results in a Mott transition and opens a Mott gap while the e-phonon interaction leads to a Peierls transition and opens a Peierls gap accompanied by a lattice deformation. We examined both transitions and studied the interplay of the two interactions. The nal ground state of an armchair CNT is discussed based on the studies of the two transitions. Next, the transport properties and energy dissipation of a two terminal carbon nanotube device are studied and the relation between the conductivity and the plasmon decay rate is explored. Particularly, the plasmon decay rate was evaluated and the correction to the conductance due to the interaction was studied in both undoped and doped case. While a uniform doping suppresses the Umklapp processes exponentially and for that reason a long armchair CNT remains metallic, in the non uniformly doped case, particularly in an armchair CNT pn junction, the relevance of the Umklapp scattering can be tuned by the doping electric eld. Depending on the steepness of the doping potential, the device can go through a quantum phase transition from a metal to insulator at zero temperature. The behavior near this critical point was studied by the epsilon expansion. At last, we studied the electron transport through a device composed of a one dimensional chain or wire connected to two graphene leads. Electrons get through the device by narrow resonance states with certain energies due to the vanishing density of states of the graphene leads at the junction. This feature of transport can be generalized to other molecular devices with graphene leads