Hitchhiking transport in quasi-one-dimensional systems

– In the conventional theory of hopping transport the positions of localized electronic states are assumed to be fixed, and thermal fluctuations of atoms enter the theory only through the notion of phonons. On the other hand, in 1D and 2D lattices, where fluctuations prevent formation of long-range order, the motion of atoms has the character of the large scale diffusion. In this case the picture of static localized sites may be inadequate. We argue that for a certain range of parameters, hopping of charge carriers among localization sites in a network of 1D chains is a much slower process than diffusion of the sites themselves. Then the carriers move through the network transported along the chains by mobile localization sites jumping occasionally between the chains. This mechanism may result in temperature independent mobility and frequency dependence similar to that for conventional hopping. Introduction. – Systems consisting of weakly coupled one-dimensional (1D) chains are ubiquitous and important. Anisotropic organic solids, polymers, columnar liquid crystals are just a few examples of quasi 1D systems important for applications. Biomaterials like DNA and proteins in many respects behave as topologically 1D systems. Because of structural and dynamic disorder, the charge transport in these materials is often due to incoherent phonon-assisted hopping of charge carriers between localized sites. Most theoretical models of hopping transport in quasi-1D systems predict a strong temperature dependence for the carrier mobility of the form μ ∼ e0 ) with α ≤ 1 for variable-range hopping near the Fermi level and α = 2 for Gaussian energy distribution of hopping sites. Although these predictions are often consistent with experiment, there are a growing number of experimental findings, mostly in soft matter systems, which are difficult to explain within conventional models of thermally-activated electron hopping. One such puzzle is temperature-independent mobility (TIM). First encountered in anisotropic organic crystals of polyacenes [1], TIM has been later observed in some other molecular crystals [2], columnar liquid crystals [3], and conjugated polymers [4]. Discussion of possible mechanisms of TIM has recently caught interdisciplinary attention after a very weak temperature dependence was reported for electron conductivity along the DNA double helix [5]. Because of the Einstein relation μ = eD/kBT , TIM implies that the diffusion coefficient D increases linearly with temperature. Such behavior is difficult to explain within conventional hopping models with the Miller-Abrahams expression for jump rates which depends