Ac hopping conduction at extreme disorder takes place on the percolating cluster

Simulations of the random barrier model show that ac currents at extreme disorder are carried almost entirely by the percolating cluster slightly above threshold; thus contradicting traditional theories contributions from isolated low-activation-energy clusters are negligible. The effective medium approximation in conjunction with the Alexander-Orbach conjecture leads to an excellent analytical fit to the universal ac conductivity with no nontrivial fitting parameters

Stretched-exponential decay functions from a self-consistent model of dielectric relaxation

There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this paper we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives.Comment: 17 page

Fracton pairing mechanism for "strange" superconductors: Self-assembling organic polymers and copper-oxide compounds

Self-assembling organic polymers and copper-oxide compounds are two classes of "strange" superconductors, whose challenging behavior does not comply with the traditional picture of Bardeen, Cooper, and Schrieffer (BCS) superconductivity in regular crystals. In this paper, we propose a theoretical model that accounts for the strange superconducting properties of either class of the materials. These properties are considered as interconnected manifestations of the same phenomenon: We argue that superconductivity occurs in the both cases because the charge carriers (i.e., electrons or holes) exchange {\it fracton excitations}, quantum oscillations of fractal lattices that mimic the complex microscopic organization of the strange superconductors. For the copper oxides, the superconducting transition temperature $T_c$ as predicted by the fracton mechanism is of the order of $\sim 150$ K. We suggest that the marginal ingredient of the high-temperature superconducting phase is provided by fracton coupled holes that condensate in the conducting copper-oxygen planes owing to the intrinsic field-effect-transistor configuration of the cuprate compounds. For the gate-induced superconducting phase in the electron-doped polymers, we simultaneously find a rather modest transition temperature of $\sim (2-3)$ K owing to the limitations imposed by the electron tunneling processes on a fractal geometry. We speculate that hole-type superconductivity observes larger onset temperatures when compared to its electron-type counterpart. This promises an intriguing possibility of the high-temperature superconducting states in hole-doped complex materials. A specific prediction of the present study is universality of ac conduction for $T\gtrsim T_c$.Comment: 12 pages (including separate abstract page), no figure

Conductance Distributions in Random Resistor Networks: Self Averaging and Disorder Lengths

The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths P(g)\simg^{\mu-1}. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of size $L$ and distribution tail parameter $\mu$. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit $\mu$ --> 0. A {\it disorder length} $\xi_D$ is identified beyond which the system is effectively homogeneous. This length diverges as $\xi_D \sim |\mu|^{-\nu}$ ($\nu$ is the regular percolation correlation length exponent) as $\mu$-->0. This suggest that exactly the same critical behavior can be induced by geometrical disorder and bu strong bond disorder with the bond occupation probability $p$$\mu$. Only lattices at the percolation threshold have renormalized probability distribution in a {\it Levy-like} basin. At the threshold the disorder length diverges at a vritical tail strength $\mu_c$ as $|\mu-\mu_c|^{-z}$, with $z=3.2\pm 0.1$, a new exponent. Critical path analysis is used in a generalized form to give form to give the macroscopic conductance for lattice above $p_c$.Comment: 16 pages plain TeX file, 6 figures available upon request.IBC-1603-01

Origin of multi-level switching and telegraphic noise in organic nanocomposite memory devices.

The origin of negative differential resistance (NDR) and its derivative intermediate resistive states (IRSs) of nanocomposite memory systems have not been clearly analyzed for the past decade. To address this issue, we investigate the current fluctuations of organic nanocomposite memory devices with NDR and the IRSs under various temperature conditions. The 1/f noise scaling behaviors at various temperature conditions in the IRSs and telegraphic noise in NDR indicate the localized current pathways in the organic nanocomposite layers for each IRS. The clearly observed telegraphic noise with a long characteristic time in NDR at low temperature indicates that the localized current pathways for the IRSs are attributed to trapping/de-trapping at the deep trap levels in NDR. This study will be useful for the development and tuning of multi-bit storable organic nanocomposite memory device systems

Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic results related to percolation: namely, the conduction properties of a large random resistor network as the fraction of resistors is varied. We focus on how the conductance of such a network vanishes as the percolation threshold is approached from above. We also discuss the more microscopic current distribution within each resistor of a large network. At the percolation threshold, this distribution is multifractal in that all moments of this distribution have independent scaling properties. We will discuss the meaning of multifractal scaling and its implications for current flows in networks, especially the largest current in the network. Finally, we discuss the relation between resistor networks and random walks and show how the classic phenomena of recurrence and transience of random walks are simply related to the conductance of a corresponding electrical network.Comment: 27 pages & 10 figures; review article for the Encyclopedia of Complexity and System Science (Springer Science

Current-Voltage Characteristics of Long-Channel Nanobundle Thin-Film Transistors: A Bottom-up Perspective

By generalizing the classical linear response theory of stick percolation to nonlinear regime, we find that the drain current of a Nanobundle Thin Film Transistor (NB-TFT) is described under a rather general set of conditions by a universal scaling formula ID = A/LS g(LS/LC, rho_S * LS * LS) f(VG, VD), where A is a technology-specific constant, g is function of geometrical factors like stick length (LS), channel length (LC), and stick density (rho_S) and f is a function of drain (VD) and gate (VG) biasing conditions. This scaling formula implies that the measurement of full I-V characteristics of a single NB-TFT is sufficient to predict the performance characteristics of any other transistor with arbitrary geometrical parameters and biasing conditions

Scaled frequency-dependent transport in the mesoscopically phase-separated colossal magnetoresistive manganite La_{0.625-y}Pr_yCa_{0.375}MnO_3

We address the issue of massive phase separation (PS) in manganite family of doped Mott insulators through ac conductivity measurements on La$_{0.625-y}$Pr$_{y}$Ca$_{0.375}$MnO$_{3}$ (0.375 $\leq$ y $\leq$ 0.275), and establish applicability of the scaling theory of percolation in the critical regime of the PS. Measurements of dc resistivity, magnetization (M(T)) and electron diffraction show incomplete growth of a ferromagnetic (FM) metallic component on cooling the high temperature charge ordered (CO) phase well below Curie temperature. The impedance $\mid$Z(T,f)$\mid$ measured over a frequency (f) range of 10 Hz to 10 MHz in the critical regime follows a universal scaling of the form $\approx$ R(T,0)g(f$\xi^{2+\theta}$) with $\theta$ $\approx$ 0.86 and the normalized correlation length varying from 1 to 4, suggesting anomalous diffusion of holes in percolating FM clusters.Comment: 12 pages and 5 figure