Localization and interactions in quasi one-dimension

Abstract

A formalism is developed to study the resistance of quasi one-dimensional wires in the localization regime with the inelastic scatterings included. At very low temperatures it is the inelastic scattering due to the interaction of the electrons with the tunnelling states (TS) that dominates. The frequency of this inelastic scattering is governed by the amount of disorder capable of producing a certain number of two-level systems (i.e. TS). Localization and interaction are thus connected in this regime in that both are governed by the amount of disorder present in the system. The whole range of disorder can be mapped in our formulation. Certain outstanding issues relevant to basic aspects of localization and interaction effects in quasi one-dimension are addressed. The electrical resistances of these systems are found to be sensitive to the frequency of the inelastic scattering events. The increment in resistance due to localization and interaction is found to depend more strongly on the bulk resistivity of the material as the inelastic scattering events reduce in their frequency of happening from over a few atomic spacings to a moderate frequency where occasionally an interaction happens over distances of the order of the localization length or a few multiples of it - the dependence changes from square-root to linear. The dependence on temperature and area of cross-section of the wire however do not show such sensitivity. We also propose that the observed temperature dependence of the phase decoherence time found in the case of disordered mesoscopic systems may be due to the fact that the TSs are interacting with one another which in turn leads to the tunnelling to become incoherent. This may limit the phase decoherence time to a finite value.