Hitchhiking transport in quasi–one-dimensional systems

Abstract

Abstract. -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 ∼ e

Quasi‐one‐dimensional systems: fluctuations, transport and interplay

“…In quasi-1D systems this periodic potential is created by adjacent chains and is not static, which makes the problem very difficult [11]. It was suggested in [1] that some insight can be achieved by modelling the chains interaction using the Langevin approach. Namely, one may assume that the force exerted on an atom by adjacent chains can be written as the sum of a regular dissipative force linear in the atom's velocity, −γq i , and a fluctuating term ξ i (t).…”

“…Next, one can show [1] that the Laplace-Fourier transform of the velocity correlation function C(ω) = ∞ 0 dt e −iωt C(t) determines the dynamical mobility µ(ω) of a charged atom,…”

“…In recent paper [1] it was suggested that since individual atoms in a 1D lattice are to some extent delocalized, they may serves as temporary vehicles for localized electrons. Consider a system of parallel chains separated by the distance b which is larger than the lattice spacing a.…”

“…In a sufficiently long chain the atomic displacement from equilibrium position q 2 i 1/2 may be significantly longer than the equilibrium lattice spacing a. For instance, for the force constant k ∼ 1 N/m, temperature T ∼ 10 2 K, and i = 10 4 the equation (1) predict the displacement of order 100 Å. In the limit of the infinite chain the MSD diverges and atomic motion is unbounded.…”

Path Integral Methods in the Su–Schrieffer–Heeger Polaron Problem

“…Hopping of electrons from site to site accompanied by a coupling to the lattice vibration modes is a fundamental process determining the transport [36] and equilibrium properties of many body systems [37]. A variable range hopping may introduce some degree of disorder thus affecting the charge mobility [38,39] and the thermodynamic functions.…”