We consider two one-dimensional interacting electron systems that are coupled via interchain tunneling to calculate transport properties in the presence of impurities or a single barrier by using the bosonization formalisms for the non-Luttinger-liquid phases on the phase diagram obtained by Fabrizio [Phys. Rev. B 48, 15 838 (1993)]. We find for the weak- and strong-interaction phases, where the superconducting correlation dominates in the ground state, that the interchain transfer enhances the conductivity and the Anderson localization is suppressed. This shows that multichain systems can have unique transport properties.
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 generalize the fermionic renormalization group method to describe analytically transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided asymmetry is not too high.
We generalize the fermionic renormalization group method to analytically describe transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T. Our approach allows us to systematically analyze the contributions to renormalized scattering amplitudes from different characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities may get strong due to a renormalization by interacting electrons, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance, provided the asymmetry is not too high.
We study the two-band model of spinless fermions in one dimension for weak repulsive interactions. In this case, the model is equivalent to the weakly interacting spinless two-leg ladder. We obtain nonuniversal analytic expressions for the power-law decays $\ensuremath{\propto}{x}^{\ensuremath{-}\ensuremath{\gamma}}$ of the charge-density and $\ensuremath{\propto}{x}^{\ensuremath{-}1/\ensuremath{\gamma}}$ of the superconducting pairing correlation functions. To leading order in the doping $\ensuremath{\delta}$ away from half filling and ${t}_{\ensuremath{\perp}}/t,$ we find $\ensuremath{\gamma}=1+({\ensuremath{\pi}}^{2}{/8)(t}_{\ensuremath{\perp}}{/t)}^{2}{\ensuremath{\delta}}^{2}$
(t and ${t}_{\ensuremath{\perp}}$ are the hopping terms along and between the chains), such that superconducting pairing correlations dominate. We furthermore show that the transition from the superconducting phase to the usual one-dimensional (Luttinger) metal occurs via a mixed phase, where superconducting pairs are formed in the bonding band only. We give the phase diagram as a function of temperature and doping.
We study the transport properties of one-dimensional (1D) interacting fermions through a barrier by numerically calculating the Kohn charge stiffness constant and the relative Drude weight. We find that the transport properties of the 1D Hubbard model are quite different from those of the 1D spinless fermion model. For example, the presence of the attractive interaction between electrons in the 1D Hubbard model actually suppresses the dc conductance, while a small repulsive interaction enhances the dc conductance. These results show that the spin degree of freedom plays an important role in the transport properties of the 1D interacting fermion systems.