Effects of disorder on two strongly correlated coupled chains

Abstract

We study the effects of disorder on a system of two coupled chain of strongly correlated fermions (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 range of parameter 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 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. 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.

Singular or non-Fermi liquids

“…This is known from calculations on ladder models [203]. Such states have also been proposed for copper-oxide compounds [148,128,58].…”

“…One of them is the "d-wave" type superconductivity and the other is the presence of phases of "orbital antiferromagnetism" for some range of parameters [203,173].…”

Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

“…As described below, it is in that respect that our theory differs from the standard two-chain problem of coupled Luttinger liquids investigated, e.g., in Refs. [48][49][50][51][52][53][54]. The standard twochain model is usually derived by coupling two Hubbard chains via a transverse hopping matrix element [55], and has been used to study, e.g., the stability of Luttinger liquid behavior with respect to interchain coupling [56][57][58].…”

Magnetic response and quantum critical behavior in the doped two-leg extended Hubbard ladder

“…It has been established that the d-wave-like superconducting (SCd) state becomes the most dominant fluctuation in the ground state of the doped two-leg Hubbard ladder and t-J ladder systems. 19,20,21,22,23,24,25,26,27,28,29,30 When the model is extended to include parameters of several intersite Coulomb repulsions, other fluctuations can overcome the SCd state. A global phase diagram obtained from a weak-coupling g-ology approach shows that the CDW state, s-wave-singlet state, and d-density-wave states can also become quasi-long-rangeordered states in parameter space.…”