Random Resistor Network Research Articles

1/ f noise in the superconducting state of quasi-two-dimensional organic conductors (BEDT–TTF) 2X—A comparative study

We report on resistance noise spectroscopy measurements in the superconducting state of two quasi-two-dimensional organic superconductors. The superconducting state of β ″ ‐ ( ET ) 2 SF 5 CH 2 CF 2 SO 3 is homogeneous, whereas κ ‐ ( ET ) 2 Cu [ N ( CN ) 2 ] Cl under pressure is located in the inhomogeneous region of the phase diagram, where antiferromanetic/insulating and superconducting phases coexist. For the latter material, the finite noise level even well below T c is understood in the framework of a random resistor network. Furthermore, the noise provides evidence for percolation-type superconductivity. For homogeneous β ″ ‐ ( ET ) 2 SF 5 CH 2 CF 2 SO 3 , however, no indications of percolation effects are found: the noise in the superconducting state vanishes and the normalized noise level S R / R 2 is generally one order of magnitude lower.

Possible origins for paramagnetic-ferromagnetic and insulator-metal transitions as well as colossal magnetoresistance in manganites

Systematical investigations of zero-field resistivity, magnetoresistance and magnetization were performed for a typical manganese compound La2/3Ca1/3MnO3. It is argued that the common origin for insulator-metal and paramagenetic ferromagnetic-transitions as well as colossal magnetoresistance is due to the formation of ferromagnetic clusters in the paramagnetic background. The transition to metallic state is resulted from percolation of ferromagnetic metallic clusters, while the colossal magnetoresistance is due to the application of magnetic field, which accelerates the growth of ferromagnetic metallic clusters and causes the shift of the onset temperature for the metallic percolation to higher temperature. Based on the random resistor network model, the zero-field resistivity versus temperature dependence is simulated by using experimental parameters, and experimental data well agree with those in whole temperature range, giving a strong support to our approach.

Anisotropic generalization of Stinchcombe's solution for the conductivity of random resistor networks on a Bethe lattice

Our study is based on the work of Stinchcombe (1974 J. Phys. C: Solid State Phys. 7 179) and is devoted to the calculations of average conductivity of random resistor networks placed on an anisotropic Bethe lattice. The structure of the Bethe lattice is assumed to represent the normal directions of the regular lattice. We calculate the anisotropic conductivity as an expansion in powers of the inverse coordination number of the Bethe lattice. The expansion terms retained deliver an accurate approximation of the conductivity at resistor concentrations above the percolation threshold. We make a comparison of our analytical results with those of Bernasconi (1974 Phys. Rev. B 9 4575) for the regular lattice.

Surface plasmon resonance of gold nanoparticles formed by cathodic arc plasma ion implantation into polymer

Shallow subsurface layers of gold nanoclusters were formed in polymethylmethacrylate (PMMA) polymer by very low energy (49 eV) gold ion implantation. The ion implantation process was modeled by computer simulation and accurately predicted the layer depth and width. Transmission electron microscopy (TEM) was used to image the buried layer and individual nanoclusters; the layer width was ∼6–8 nm and the cluster diameter was ∼5–6 nm. Surface plasmon resonance (SPR) absorption effects were observed by UV-visible spectroscopy. The TEM and SPR results were related to prior measurements of electrical conductivity of Au-doped PMMA, and excellent consistency was found with a model of electrical conductivity in which either at low implantation dose the individual nanoclusters are separated and do not physically touch each other, or at higher implantation dose the nanoclusters touch each other to form a random resistor network (percolation model).

Conduction in rectangular quasi-one-dimensional and two-dimensional random resistor networks away from the percolation threshold

In this study we investigate electrical conduction in finite rectangular random resistor networks in quasione and two dimensions far away from the percolation threshold p(c) by the use of a bond percolation model. Various topologies such as parallel linear chains in one dimension, as well as square and triangular lattices in two dimensions, are compared as a function of the geometrical aspect ratio. In particular we propose a linear approximation for conduction in two-dimensional systems far from p(c), which is useful for engineering purposes. We find that the same scaling function, which can be used for finite-size scaling of percolation thresholds, also applies to describe conduction away from p(c). This is in contrast to the quasi-one-dimensional case, which is highly nonlinear. The qualitative analysis of the range within which the linear approximation is legitimate is given. A brief link to real applications is made by taking into account a statistical distribution of the resistors in the network. Our results are of potential interest in fields such as nanostructured or composite materials and sensing applications.

Distribution functions in percolation problems

Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various such distribution functions in the limits where certain scaling variables become small or large. Our study includes the pair-connection probability, the distributions of the fractal masses of the backbone, the red bonds, and the shortest, the longest, and the average self-avoiding walk between any two points on a cluster, as well as the distribution of the total resistance in the random resistor network. Our analysis draws solely on general, structural features of the underlying diagrammatic perturbation theory, and hence our main results are valid to arbitrary loop order.

Linear magnetoresistance inAg2+δSethin films

In the nonstoichiometric low-temperature phase of silver selenide a very small silver excess within the semiconducting silver selenide matrix in the order of 0.01% is sufficient to generate a linear magnetoresistance (LMR) of more than 300% at 5 T, which does not saturate at fields up to 60 T. Different theoretical models have been proposed to explain this unusual magnetoresistance (MR) behavior, among them a random resistor network consisting of four-terminal resistor units. According to this model the LMR and the crossover field from linear to quadratic behavior are primarily controlled by both the spatial distribution of the charge-carrier mobility and its average value, being essentially functions of the local and average compositions. Here we report measurements on silver-rich thin ${\text{Ag}}_{x}\text{Se}$ films with a thickness between 20 nm and $2\text{ }\ensuremath{\mu}\text{m}$, which show an increasing average mobility in conjunction with an enhanced MR for increasing film thickness. We found a linear scaling between the size of the transverse LMR and the crossover field, as predicted by the theory. For films thinner than about 100 nm the MR with field directed in the sample plane shows a breakdown of the LMR, revealing the physical length scale of the inhomegeneities in thin ${\text{Ag}}_{x}\text{Se}$ devices.

Second harmonic generation in random nonlinear dielectrics: Effective medium approximations and dilute limit expressions

Based on a general expression previously derived for the effective coefficient for second harmonic generation (SHG) in a random composite of nonlinear dielectrics, we develop and compare several possible effective medium approximations (EMAs). The general expression involves the volume average of products of local field factors of the form ⟨EωEωE2ω⟩, and the three EMAs amount to different decoupling schemes, and they all invoke the EMA for a linear binary composite. The performance of these EMAs is assessed by comparing with numerical results obtained by simulations on random resistor networks. We also derived the corresponding dilute limit expressions for each of the EMAs. The expressions differ in the terms that are proportional to the SHG coefficient of the majority component, and the different decoupling schemes give different terms that are quadratic in the dielectric contrast between the linear dielectric constants of the two constituents at the fundamental and second harmonic frequencies.

Diffusion and localization in quantum random resistor networks

The theoretical description of transport in a wide class of novel materials is based upon quantum-percolation and related random-resistor-network (RRN) models. We examine the localization properties of electronic states of diverse two-dimensional quantum-percolation models using exact diagonalization in combination with kernel-polynomial-expansion techniques. Employing the local-distribution approach, we determine the arithmetically and geometrically averaged densities of states in order to distinguish extended, current-carrying states from localized ones. To get further insight into the nature of eigenstates of RRN models, we analyze the probability distribution of the local density of states in the whole parameter and energy range. For a recently proposed RRN representation of graphene sheets, we discuss leakage effects.

Relaxation phenomena at the metal-to-insulator transition in La 0.8Sr 0.2MnO 3 single crystals

The time dependence of the resistance R A C of a La 0.8Sr 0.2MnO 3 single crystal has been investigated in the vicinity of the metal-to-insulator transition temperature. We used local probe microscopy to show the existence, at room temperature, of coexisting clusters of micrometer size. Our analysis shows that relaxation effects can be described with a simple exponential contribution using a random resistor-network, based on phase separation between insulating and metallic domains. Our results clearly prove the existence of a percolation threshold over which no percolation path exists. Moreover, these results highlight the significant role of the remanent magnetization.

Electronic Shot Noise in Fractal Conductors

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.

Strain effects on percolation conduction in conductive particle filled composites

The effect of uniaxial and multiaxial mechanical strain on the electrical conductivity of particle filled polymer composites is investigated in the framework of concentration-driven percolation. For composites consisting of low aspect ratio, rigid conductive particles in a compliant polymer matrix, a simple argument leads to the conclusion that the effective volume fraction of conductive particles (the ratio of total particle volume to the total volume of the deformed composite) plays a dominant role, with conductivity remaining isotropic despite the directional bias of the strain state. As such, conductivity is expected to exhibit classical power, law-dependence on concentration, which in this case takes the form of a strain-dependent effective volume fraction. Consideration of deformation effects on particle agglomerates suggest, however, that particle-to-particle network connections are likely to be affected most significantly along directions experiencing the most severe strains, introducing a directional bias in network connectivity at a higher length scale. To assess the importance of this possible directional bias, random resistor network models are used to study the conductivity of uniaxially strained composites. For conservative assumptions on the severity of the bias in bond probabilities, network conductivities exhibit approximately isotropic, concentration-driven behavior for moderate strains, supporting the predictive utility of the simple percolation conduction-effective volume fraction approach. Further corroboration is provided by experiments in the literature on silicone-graphite composites subjected to uniaxial compressive strain, where good agreement is obtained through moderate strains for the theoretically correct value of the conduction exponent in concentration-driven percolation.

Scaling laws for nanoFET sensors

The sensitive conductance change of semiconductor nanowires and carbon nanotubes inresponse to the binding of charged molecules provides a novel sensing modality which isgenerally denoted as nanoFET sensors. In this paper, we study the scaling laws ofnanoplate FET sensors by simplifying nanoplates as random resistor networks withmolecular receptors sitting on lattice sites. Nanowire/tube FETs are included as thelimiting cases where the device width goes small. Computer simulations show that the fieldeffect strength exerted by the binding molecules has significant impact on the scalingbehaviors. When the field effect strength is small, nanoFETs have little size and shapedependence. In contrast, when the field effect strength becomes stronger, thereexists a lower detection threshold for charge accumulation FETs and an upperdetection threshold for charge depletion FET sensors. At these thresholds, thenanoFET devices undergo a transition between low and large sensitivities. Thesethresholds may set the detection limits of nanoFET sensors, while they could beeliminated by designing devices with very short source–drain distance and large width.

Random Resistor Network Model of Minimal Conductivity in Graphene

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.

Nonlinear DC conduction behavior in epoxy resin/graphite nanosheets composites

Epoxy resin (ER)/graphite nanosheet (GN) composites with a low percolation threshold (owing to particular geometry of GN with the high aspect ratio) were fabricated. The nonlinear conduction behavior of ER/GN composites above the percolation threshold by the action of variable DC electrical field was investigated. For specimens, the current density or current reduces with decreasing graphite nanosheets concentrations, and the J– E curves are well fitted by a cubic, J= σ 1 E+ σ 3 E 3. Moreover, the crossover current density J c, at which nonlinearity takes place, scales with the linear conductivity σ 1 as J c ∼ σ 1 x , with x≈1.390 and the third-order conductivity, σ 3, also scales with J c as J c ∼ σ 3 y , with y≈1.175. Through the discussion of the nonlinearity within the framework of two theoretical models, the nonlinear random resistor network (NLRRN) and the dynamic random resistor network (DRRN), it is indicated that neither of these two models can fully explain our experimental results. Taking into account the microscopic structures and conduction processes of the composites, it is likely that a combination of these two models explain the nonlinear characteristics better.

Nonsaturating magnetoresistance of inhomogeneous conductors: Comparison of experiment and simulation

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and nonsaturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as 10μm. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random-resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag_(2±δ)Se and Ag_(2±δ)Te, in magnetic fields up to 55T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments.

Synchronization in weighted uncorrelated complex networks in a noisy environment: Optimization and connections with transport efficiency

Motivated by synchronization problems in noisy environments, we study the Edwards-Wilkinson process on weighted uncorrelated scale-free networks. We consider a specific form of the weights, where the strength (and the associated cost) of a link is proportional to (kikj)beta with ki and kj being the degrees of the nodes connected by the link. Subject to the constraint that the total edge cost is fixed, we find that in the mean-field approximation on uncorrelated scale-free graphs, synchronization is optimal at beta*= -1 . Numerical results, based on exact numerical diagonalization of the corresponding network Laplacian, confirm the mean-field results, with small corrections to the optimal value of beta*. Employing our recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, we also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted routing schemes.

Mesoscale models of ac conductivity in composite polymeric electrolytes

The presented paper shows a possibility of creation of a useful and efficient model of conductivity for composite polymeric electrolytes. It deals with a more elaborate and versatile mesoscale approach (in comparison to the already applied Effective Medium Theory approach for which each new composite microstructure forces a new mixing rule development) based on the Random Resistor Network method. The introduced model can predict the ac conductivity values for a whole spectrum of frequencies for different composites with a wide range of possible microstructures. It is based on complex current iteration procedure for a randomly generated three-dimensional network of impedances constituting a digital image of the electric properties of the virtual sample studied. A spatial unit of the material present in the sample is defined as a parallel RC connection.

Mesoscale models of conductivity in polymeric electrolytes—A comparative study

The studies of conductivity behavior of composite polymeric electrolytes (CPE) have been widely realized for about 15 years. There is, however, a lack of a versatile and efficient model of conductivity in these systems. The effective medium approach was introduced to predict the conductivity of systems according to some previously defined mixing rules. The main limitation of this method, however, is the fact that each new composite microstructure forces a new mixing rule development. This paper presents the random resistor network approach as an alternative method to the effective medium theory based approach. The presented comparison of both methods is based on both dc and ac simulated conductivity data. Some experimental data are introduced to compare the models with the conductivity values obtained for real samples.

Random Resistor Network Approach to Modeling of Conductivity in Composite Polymeric Electrolytes.

There is lack of a versatile and efficient model of conductivity for composite polymeric electrolytes. The main limitation of the already applied Effective Medium Theory approach is the fact that each new composite microstructure forces a new mixing rule development. This paper deals with a more elaborate and versatile approach based on the Random Resistor Network method. The introduced model yields simulated conductivity values for composites of any possible microstructure. It is based on current iteration procedure for a randomly generated three dimensional resistor network constituting a digital image of the sample studied. Both the d.c. conductivity value and bulk a.c response of the composite can be calculated. For a.c. studies, the resistors in the network nodes are exchanged for parallel RC or R(CPE) (constant phase element) connections. Additionally, the temperature dependence of the conductivity of the composite can be predicted on basis of the experimentally determined conductivities of the particular phases.