We study the effects of disorder on a system of two coupled chains of strongly correlated fermions (the ladder system), using a renormalization-group technique. The stability of the phases of the pure system has been investigated as a function of interactions both for fermions with spin and spinless fermions. For spinless fermions the repulsive side is strongly localized whereas the system with attractive interactions is stable with respect to disorder, at variance with the single-chain case. For fermions with spins, the repulsive side is also localized, and in particular the
d-wave superconducting phase found for the pure system is totally destroyed by an arbitrarily small amount of disorder. On the other hand, the attractive side is again remarkably stable with respect to localization. We have also computed the charge stiffness, the localization length, and the temperature dependence of the conductivity for the various phases. In the parameter range where
d-wave superconductivity would occur for the pure system the conductivity is found to decrease monotonically with temperature, even at high temperature, and we discuss this surprising result. For a model with one-site repulsion and nearest-neighbor attraction, the most stable phase is an orbital antiferromagnet. Although this phase has no divergent superconducting fluctuation it can have a divergent conductivity at low temperature. Finally, to make a comparison of our results with experimental ladder systems, we treated the interladder coupling in a mean-field approximation. We argue based on our results that the superconductivity observed in some of these compounds cannot be a simple stabilization of the
d-wave phase found for a pure single ladder. The application of our results to systems such as quantum wires is also discussed. In particular, the corrections to conductance in a two-channel quantum wire have been obtained as a function of system length, temperature, and interactions.
We investigate electron transport in disordered Hubbard chains contacted to macroscopic leads, via the nonequilibrium Green's function technique. We observe a crossover of currents and conductances at finite bias which depends on the relative strength of disorder and interactions. We provide a proof that the coherent potential approximation, a widely used method for treating disorder averages, fulfills particle conservation at finite bias with or without electron correlations. Finally, our results hint that the observed trends in conductance due to interactions and disorder also appear as signatures in the single-site entanglement entropy.