A theoretical study of the effects of disorder on the Mn-Mn exchange interactions for Ga1-xMn xAs diluted magnetic semiconductors is presented. The disorder is intrinsically considered in the calculations, which are performed using an ab initio total energy density-functional approach, for a 128 atoms supercell, and by considering a variety of configurations with 2, 3 and 4 Mn atoms. Results are obtained for the effective J$^{Mn-Mn}_n$, from first (n = 1) all the way up to sixth (n = 6) neighbors via a Heisenberg Hamiltonian used to map the magnetic excitations from ab initio total energy calculations. One then obtains a clear dependence in the magnitudes of the J$^{Mn-Mn}_n$ with the Mn concentration x. Moreover, we show that, in the case of fixed Mn concentration, configurational disorder and/or clustering effects lead to large dispersions in the Mn-Mn exchange interactions. Also, calculations for the ground-state total energies for several configurations suggest that a proper consideration of disorder is needed when one is interested in treating temperature and annealing effects.

We describe a procedure to calculate charge transport properties across a nanosystem. This scheme is based on a Green's Function formalism to treat a non-equilibrium problem, coupled to the Density Functional Theory to describe the electronic structure. As an illustration, we perform calculations for the charge transport across a (5,5) carbon nanotube with a vacancy.