Quantum transport in nanostructures

This dissertation deals with advanced computational concepts for quantum transport and spintronics in graphene and magnetic tunnel junctions. The first part is devoted to developing generic transport algorithms, applicable to any tightbinding Hamiltonian. After a review of Green's function based quantum transport formalisms, the dissertation presents a numerically stable algorithm for computing the surface Green's function of a lead, as well as a generalized Fisher-Lee relation. A matrix reordering algorithm is introduced to extend the applicability of established quantum transport algorithms. The second part discusses spin-dependent transport in magnetic tunnel junctions and graphene nanoribbons, making use of the numerical techniques developed in the first part as well as analytical models. In particular, this includes an investigation of the tunneling anisotropic magnetoresistance in a strong magnetic field, a thorough discussion of the transport in the graphene edge state, and a study of spin currents in rough graphene nanoribbons.