Electron transport, interaction and spin in graphene and graphene nanoribbons

Since the isolation of graphene in 2004, this novel material has become the major object of modern condensed matter physics. Despite of enormous research activity in this field, there are still a number of fundamental phenomena that remain unexplained and challenge researchers for further investigations. Moreover, due to its unique electronic properties, graphene is considered as a promising candidate for future nanoelectronics. Besides experimental and technological issues, utilizing graphene as a fundamental block of electronic devices requires development of new theoretical methods for going deep into understanding of current propagation in graphene constrictions. This thesis is devoted to the investigation of the effects of electronelectron interactions, spin and different types of disorder on electronic and transport properties of graphene and graphene nanoribbons. In paper I we develop an analytical theory for the gate electrostatics of graphene nanoribbons (GNRs). We calculate the classical and quantum capacitance of the GNRs and compare the results with the exact selfconsistent numerical model which is based on the tight-binding p-orbital Hamiltonian within the Hartree approximation. It is shown that electronelectron interaction leads to significant modification of the band structure and accumulation of charges near the boundaries of the GNRs. It’s well known that in two-dimensional (2D) bilayer graphene a band gap can be opened by applying a potential difference to its layers. Calculations based on the one-electron model with the Dirac Hamiltonian predict a linear dependence of the energy gap on the potential difference. In paper II we calculate the energy gap in the gated bilayer graphene nanoribbons (bGNRs) taking into account the effect of electron-electron interaction. In contrast to the 2D bilayer systems the energy gap in the bGNRs depends non-linearly on the applied gate voltage. Moreover, at some intermediate gate voltages the energy gap can collapse which is explained by the strong modification of energy spectrum caused by the electron-electron interactions. Paper III reports on conductance quantization in grapehene nanoribbons subjected to a perpendicular magnetic field. We adopt the recursive Green’s function technique to calculate the transmission coefficient which