Percolation-type Transition Research Articles

Nature of the Metal Insulator Transition in High-Mobility 2D_Si-MOSFETs.

Our investigation focuses on the analysis of the conductive properties of high-mobility 2D-Si-MOSFETs as they approach the critical carrier density, nsc (approximately 0.72×1011 cm-2), which marks the metal insulator transition (MIT). In close proximity to the nsc, the conductivity exhibits a linear dependence on the temperature (T). By examining the extrapolated conductivity at the absolute zero temperature (T = 0), denoted as σ0, as a function of the electron density ns, we identify two distinct regimes with varying σ0(ns) patterns, indicating the existence of two different phases. The transition from one of these two regimes to another, coinciding with nsc, is abrupt and serves as the focus of our investigation. Our aim is to establish the possibility of a percolation type transition in the 2D-Si-MOSFETs' sample. In fact, we observed that the model of percolation is applicable only for densities very close to nsc*=n2 (where n2 is the linear extrapolation of σ0), indicating the percolation type transition essentially represents a phase transition at the zero temperature.

Probing the electron states and metal-insulator transition mechanisms in molybdenum disulphide vertical heterostructures.

The metal-insulator transition is one of the remarkable electrical properties of atomically thin molybdenum disulphide. Although the theory of electron-electron interactions has been used in modelling the metal-insulator transition in molybdenum disulphide, the underlying mechanism and detailed transition process still remain largely unexplored. Here we demonstrate that the vertical metal-insulator-semiconductor heterostructures built from atomically thin molybdenum disulphide are ideal capacitor structures for probing the electron states. The vertical configuration offers the added advantage of eliminating the influence of large impedance at the band tails and allows the observation of fully excited electron states near the surface of molybdenum disulphide over a wide excitation frequency and temperature range. By combining capacitance and transport measurements, we have observed a percolation-type metal-insulator transition, driven by density inhomogeneities of electron states, in monolayer and multilayer molybdenum disulphide. In addition, the valence band of thin molybdenum disulphide layers and their intrinsic properties are accessed.

The Observation of a Percolation-Induced 2D Metal-Insulator Transition in AlAs

The nature of the metal-insulator transition at zero magnetic field in two-dimensional systems has remained a controversial enigma since the pioneering realization of the metallic behavior in high mobility Si-MOSFETs. In this paper the density (n) dependence of the conductivity of the two-dimensional electron gas in aluminum arsenide was analyzed in the metallic side (n ≥ 0.59×10^(11) cm^(-2)) at very low temperature. Our study reveals an inhomogeneity driven percolation type transition to an insulating state due to the breakdown of screening in the random charged impurities disordered background. The critical density found under this assumption is lower than that assumed by observing the sign of the temperature coefficient of conductivity. Experimental data are reprinted with permission from [S. J. Papadakis and M. Shayegan, Phys. Rev. B 57, R15068 (1998)].

Density inhomogeneity driven metal–insulator transition in 2D p-GaAs

In this work, we present a study of the temperature and carriers density dependence of the electrical transport of high mobility two dimensional hole system grown on the (311) surface of GaAs. At low temperatures, the analysis of the variation of conductivity data as σ(ps)∝(ps−psc⁎)δ shows that a density inhomogeneity in the metallic phase leading to percolation-type transition to an insulating state at a critical density psc⁎ that decrease slowly with increasing temperature and found to be lower than the corresponding estimate psc based on the sign of the slope dρ/dT. The experimental values of the exponent δexp are close to theoretical values corresponding to the 2D percolation transition (δth=4/3).

Electric field driven destabilization of the insulating state in nominally pure LaMnO3

We report an electric field driven destabilization of the insulating state in nominally pure LaMnO3 single crystal with a moderate field which leads to a resistive state transition below 300 K. The transition is between the insulating state in LaMnO3 and a high resistance bad metallic state that has a temperature independent resistivity. The transition occurs at a threshold field (Eth) that shows a steep enhancement on cooling. While at lower temperatures the transition is sharp and involves a large change in resistance, it softens on heating and is eventually absent above 280 K. When the Mn4+ content is increased by Sr substitution up to x = 0.1, the observed transition, although observable in a certain temperature range, softens considerably. This observation has been explained as a bias driven percolation type transition between two co-existing phases, where the majority phase is a charge and orbitally ordered polaronic insulating phase and the minority phase is a bad metallic phase. The mobile fraction f of the bad metallic phase deduced from the experimental data follows an activated kinetics as f = fo(E)exp(−Δ/kBT) with the activation energy Δ ≈ 200 meV, and the pre-factor fo(E) is a strong function of the field that leads to a rapid enhancement of f on application of field, leading to the resistive state transition. We suggest likely scenarios for such co-existing phases in nominally pure LaMnO3 that can lead to the bias driven percolation type transition.

The sigmoidal average – a powerful tool for predicting the thermal conductivity of composite ceramics

The sigmoidal average between the upper and lower Hashin-Shtrikman bounds is shown to be the appropriate average relation for isotropic two-phase composites consisting of geometrically equivalent grains. This average ensures that the prediction is close the upper bound for low volume fractions of the low-conductivity phase (corresponding to low-conductivity inclusions in a high-conductivity matrix) and vice versa. In the intermediate concentration range the sigmoidal average reflects the fact that the microstructure is bicontinuous and can undergo a percolation-type transition. It is shown that the sigmoidal average of the Hashin-Shtrikman bounds lies automatically within the three-point bounds (Miller bounds) for a practically important class of microstructures (symmetric-cell materials with spherical cells) and that in the infinite-phase-contrast case (porous media) it is close to the exponential relation, which has been very successful in describing the porosity dependence of properties. Theoretical predictions are compared with experimentally measured values for alumina-zirconia composites in the whole range of volume fractions, from pure alumina to pure zirconia. Even after appropriate correction for porosity, essentially all experimental data are below the sigmoidal average. The fact that some values are even below the lower Hashin-Shtrikman bound is indicative of microcracking and / or grain size (interface) effects.

Phosphatidyl Serine Containing Liposomes on Titania: Phase Behaviour, Bilayer Formation, and Lipid Asymmetry

Interactions between surfaces of inorganic materials and biological systems are important in numerous technological contexts (implant integration, biosensor development). They also present basic challenges. For example, the role of surface ion equilibrium in the biological response to the material is not well understood, although a casual link between the two has been proposed. Here, we investigate the behaviour of phosphatidyl serine (PS)-containing liposomes on TiO2 as a function of liposome PS contents and solution Ca2+ concentration. We determine a “phase diagram”, where a percolation-type transition between adsorbed liposomes and supported bilayers is observed, describe the driving force for this transition, and identify the role of surface heterogeneities in this porcess. Finally, we quantify the distribution of PS in the resulting supported bilayers by neutron reflectometry.

Transport and Percolation in a Low-Density High-Mobility Two-Dimensional Hole System

We present a study of the temperature and density dependence of the resistivity of an extremely high quality two-dimensional hole system grown on the (100) surface of GaAs. For high densities in the metallic regime (p > or approximately4x10;{9} cm;{-2}), the nonmonotonic temperature dependence ( approximately 50-300 mK) of the resistivity is consistent with temperature dependent screening of residual impurities. At a fixed temperature of T=50 mK, the conductivity versus density data indicate an inhomogeneity driven percolation-type transition to an insulating state at a critical density of 3.8x10;{9} cm;{-2}.

Rheological properties of gellan, κ-carrageenan and alginate polysaccharides: effect of potassium and calcium ions on macrostructure assemblages

The effect of added ions (0.5 mM K + or 0.25 mM Ca 2+) on the critical overlap ( C*) and gelation ( C o′) concentrations for gellan, κ-carrageenan and alginate polysaccharides were investigated using steady shear rheometry. Both C* and C o′ decreased for all solutions with added salts, a trend more pronounced for gellan and alginate with added Ca 2+, and κ-carrageenan with added K +. Aggregation near the sol–gel transition was modeled as a percolation-type transition. In addition, the frequency dependence of the viscoelastic storage ( G′) and loss ( G″) moduli for bulk and localized areas within a 0.7% (w/w) gellan sol were measured using a controlled stress and oscillating magnetic bead rheometer, respectively. Flow behavior of the bulk was in the terminal and plateau relaxation regions of the viscoelastic spectrum, whereas localized behavior was in the plateau and rubber–glass transition regions.

Field cooled and zero field cooled 207Pb NMR and the local structure of relaxor PbMg1/3Nb2/3O3.

An isotropic 207Pb NMR spectrum corresponding to the glassy matrix with spherical shell type Pb shifts from the cubic sites, as well as an anisotropic spectral component corresponding to polar nanoclusters with a Pb shift parallel to the [111] direction, have been observed in a PbMg(1/3)Nb(2/3)O3 (PMN) single crystal. This represents a microscopic confirmation of the model of relaxors first proposed by Burns and Dacol. A sudden increase in the intensity of the anisotropic cluster line is seen for electric fields larger than the critical field around 210 K. This demonstrates the occurrence of an orientational percolation type transition to the field-induced ferroelectric phase with about 50% of the Pb nuclei still remaining in the spherical glass matrix. A similar though smaller increase of the intensity of this line is also seen in the zero field cooled data, demonstrating that relaxor PMN is an incipient ferroelectric.

Intrinsic stresses and mechanical properties of Ti-containing hydrocarbon coatings

A detailed examination of the intrinsic stress development within and mechanical properties of Ti containing hydrocarbon (Ti–C:H) coatings deposited in an inductively coupled plasma assisted hybrid chemical vapor deposition/physical vapor deposition environment has been carried out, combining in situ substrate curvature measurements with plasma probe measurements, ex situ electrical resistivity measurements, and instrumented nanoindentation measurements. Intrinsic stresses within Ti–C:H have been found to be compressive over wide ranging compositions and plasma parameters. The intrinsic compression within Ti–C:H was found to depend significantly on the Ti composition, and was related to a percolation type transition in the nanoscale structure. The intrinsic compression within Ti–C:H has further been shown to be significantly influenced by the energy of ionic species bombarding the substrate during growth. Measured stress–thickness history was discussed in terms of possible mechanisms contributing to intrinsic stress generation. Although there are likely multiple mechanisms influencing intrinsic stress development, our present results suggest that ion bombardment plays a significant role in intrinsic stress generation within Ti–C:H, and is likely to influence stress development in other low temperature deposited amorphous hydrocarbon based ceramic nanocomposite coatings.

Thickness dependent phase separation in La0.7Ca0.3MnO3 films

The complex dielectric function of La0.7Ca0.3MnO3 films with various thicknesses and on different substrates was determined by the analysis of measured ellipsometric parameters. The temperature-dependent redistribution of low-energy spectral weight shows that the metallicity is developed gradually below an onset temperature that is found to depend strongly on global and local strain properties, not on film thickness alone. Importantly, the 2 nm film shows no metallic conduction but an optical charge-carrier response below 240 K. This suggests that ultrathin films are characterized by phase separation and a percolation-type transition.

Intrinsic stress development in Ti–C:H ceramic nanocomposite coatings

The development of intrinsic stresses within titanium-containing hydrocarbon (Ti–C:H) nanocomposite coatings was monitored during growth by in situ substrate curvature measurements using a multibeam optical sensing technique. Stress as a function of coating thickness was measured in a wide range of specimens, from nearly pure amorphous hydrocarbon (a-C:H) to nearly pure titanium carbide (TiC). The intrinsic stress within the nanocomposite coating was found to vary significantly in magnitude, and to depend systematically on the Ti composition. The observed stress variation as a function of the Ti composition correlates well with a previously reported percolation-type transition in the coating microstructure.

Modelling the percolation-type transition in radiation damage

Following the concept of percolation-type transition in zircon under radiation damage suggested previously, the general simulation model of irradiated material is proposed. The model naturally gives rise to swelling of the undamaged crystalline part of irradiated material. X-ray scattering profiles are calculated and show broadening that increases with radiation damage, in good agreement with published experimental x-ray diffraction data on zircon. The effect of percolation on material bulk properties is studied.

Mechanical characterization of network formation during heat-induced gelation of whey protein dispersions.

The formation of gel network structures during isothermal heating of whey protein aqueous dispersions was probed by mechanical spectroscopy. It was anticipated that the pathway of the sol-to-gel transition of whey protein dispersions is quite different from that of ordinary cross-linking polymers (e.g., percolation-type transition), since aqueous solutions of native whey proteins have been shown to be highly structured even before gelation, in our previous study. At 20 degrees C, aqueous dispersions of beta-lactoglobulin, the major whey protein, and those of whey protein isolate (WPI), a mixture of whey proteins, exhibited solid-like mechanical spectra, i.e., the predominant storage modulus G' over the loss modulus G", in a certain range of the frequency omega (1-100 rad/s), regardless of the presence or absence of added NaCl. The existence of the added salt was, however, a critical factor for determining transitions in mechanical spectra during gelation at 70 degrees C. beta-Lactoglobulin dispersions in 0.1 mol/dm(3) NaCl maintained the solid-like nature during the entire gelation process and, after passing through the gelation point, satisfied parallel power laws (G' approximately G" approximately omega(n)) that have been proposed for a critical gel (i.e., the gel at the gelation point) that possesses a self-similar or fractal network structure. In contrast, beta-lactoglobulin dispersions without added salt exhibited a transition from solid-like [G'(omega) > G"(omega)] to liquid-like [G'(omega) < G"(omega)] mechanical spectra before gelation, but no parallel power law behavior was recognized at the gelation point. During extended heating time (aging), beta-lactoglobulin gels with 0.1 mol/dm(3) NaCl showed deviations from the parallel power laws, while spectra of gels without added NaCl approached the parallel power laws, suggesting that post-gelation reactions also significantly affect gel network structures. A percolation-type sol-to-gel transition was found only for WPI dispersions without added salt.

Optical investigations ofLa7/8Sr1/8MnO3

We investigated temperature dependent optical conductivity spectra of La_{7/8}Sr_{1/8}MnO_3. Its phonon bending mode starts to be splitted near a structural phase transition temperature. With further cooling, strength of a mid-infrared small polaron peak, which is located at 0.4 eV, becomes increased. These temperature dependent changes in the phonon spectra and the polaron absorption peaks were explained by a phase separation and a percolation-type transition.

Frustration, connectivity, and the glass transition

The concepts of connectivity, localization, and frustration are explored in relation to glass formation in amorphous materials. First, the concept of eigenclusters to geometrically characterize correlations in amorphous materials is introduced, and discussed in detail for both the Ising ferromagnet and Ising spin glass models. Second, a new, glass-forming percolation model that contains frustration as the essential ingredient, and exhibits two percolation transitions, is discussed. This new model gives new insights into frustrated systems, and applications to the Ising spin glass model and other glass-forming systems are discussed. In particular, we propose the possibility that the occurrence of a percolation-type transition at temperatures above the glass transition temperature may be a general feature of glass-forming systems. The important role of computer simulations in probing the mechanism of glass formation is emphasized.

Transport of excitations in disordered systems: Self-consistent density resummation

New self-consistent equations for the transport of excitations in disordered systems are derived based on a resummation procedure of the density expansion. Both local-time [partial-time-ordering prescription (POP)] and convolution-type [chronological-time-ordering prescription] equations are explored. Application is made to a system consisting of a random mixture of donors and traps with a general type of transfer rate $W(r)$. We calculate the probability of remaining in the original site ${G}_{0}(t)$ as well as the second moment of the distribution of excitations $〈{r}^{2}(t)〉$. The POP equations reduce to the exact Forster solution for ${G}_{0}(t)$ in the case of traps only. We analyze the long-time behavior of ${G}_{0}(t)$ and its dependence on $W(r)$. We find a percolation-type transition when $W(r)$ has a cutoff [i.e., $W(r)=0$ for $r&gt;{r}_{0}$] but in all other cases the system is diffusive at long times [${G}_{0}(t)$ vanishes and $〈{r}^{2}(t)〉$ diverges linearly in time].

Transport and percolation in disordered systems?A self-consistent time-local approach

A new self-consistent equation for the transport of excitations in disordered systems, which forms the basis for a new class of time-domain coherent potential approximations, is developed. As an example, we calculate the probability of remaining in the original site G0(t) as well as the second moment of the distribution of excitations 〈r2(t)〉 for a random mixture of donors which satisfy a master equation with short-range transition rates. A percolation-type transition is observed and its characteristics are analyzed both above and below the transition point.