arXiv subjects

A. N. Samukhin

Publications and source records attributed to A. N. Samukhin.

22 records · Page 2Linked to original sources

arXiv2000

On dispersive energy transport and relaxation in the hopping regime

A new method for investigating relaxation phenomena for charge carriers hopping between localized tail states has been developed. It allows us to consider both charge and energy {\it dispersive} transport. The method is based on the idea of quasi-elasticity: the typical energy loss during a hop is much less than all other characteristic energies. We have investigated two models with different density of states energy dependencies with our method. In general, we have found that the motion of a packet in energy space is affected by two competing tendencies. First, there is a packet broadening, i.e. the dispersive energy transport. Second, there is a narrowing of the packet, if the density of states is depleting with decreasing energy. It is the interplay of these two tendencies that determines the overall evolution. If the density of states is constant, only broadening exists. In this case a packet in energy space evolves into Gaussian one, moving with constant drift velocity and mean square deviation increasing linearly in time. If the density of states depletes exponentially with decreasing energy, the motion of the packet tremendously slows down with time. For large times the mean square deviation of the packet becomes constant, so that the motion of the packet is ``soliton-like''.

cond-mat.dis-nn↗

arXiv1998

Hopping Conductivity of a Nearly-1d Fractal: a Model for Conducting Polymers

We suggest treating a conducting network of oriented polymer chains as an anisotropic fractal whose dimensionality D=1+εis close to one. Percolation on such a fractal is studied within the real space renormalization group of Migdal and Kadanoff. We find that the threshold value and all the critical exponents are strongly nonanalytic functions of εas εtends to zero, e.g., the critical exponent of conductivity is ε^{-2}\exp (-1-1/ε). The distribution function for conductivity of finite samples at the percolation threshold is established. It is shown that the central body of the distribution is given by a universal scaling function and only the low-conductivity tail of distribution remains $ε$-dependent. Variable range hopping conductivity in the polymer network is studied: both DC conductivity and AC conductivity in the multiple hopping regime are found to obey a quasi-1d Mott law. The present results are consistent with electrical properties of poorly conducting polymers.

cond-mat.dis-nn↗

arXiv1997

Conductivity fluctuations in polymer's networks

Polymer's network is treated as an anisotropic fractal with fractional dimensionality D = 1 + εclose to one. Percolation model on such a fractal is studied. Using the real space renormalization group approach of Migdal and Kadanoff we find threshold value and all the critical exponents to be strongly nonanalytic functions of ε, e.g. the critical exponent of the conductivity was obtained to be ε^{-2}\exp(-1-1/ε). The main part of the finite size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable, which is proportional to the large power of the conductivity, but with dimensionally-dependent low-conductivity cut-off. Its reduced central momenta are of the order of \exp(-1/ε) up to the very high order.

cond-mat.dis-nn↗

arXiv1996

Critical Percolation and Transport in Nearly One Dimension

A random hopping on a fractal network with dimension slightly above one, $d = 1 + ε$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of Migdal and Kadanoff, the critical behavior near the percolation threshold is studied. In contrast to a conventional regular expansion in $ε$, the critical indices of correlation length, $ν=ε^{-1}+O(e^{-1/ε})$, and of conductivity, $t\simeq ε^{-2} exp (-1-1/ε)$, are found to be nonanalytic functions of $ε$ as $ε\to 0$. Distribution for conductivity of the critical cluster is obtained to be gaussian with the relative width $\sim \exp (-1/ε)$. In case of variable range hopping an ``1-d Mott's law'' $exp [ -( T_t/T)^{1/2}]$ dependence was found for the DC conductivity. It is shown, that the same type of strong temperature dependence is valid for the dielectric constant and the frequency-dependent conductivity, in agreement with experimental data for poorly conducting polymers.

cond-mat.dis-nn↗