Two-dimensional Localization Research Articles

Anderson localization problem: An exact solution for 2-D anisotropic systems

Our previous results [V.N. Kuzovkov, W. von Niessen, V. Kashcheyevs, O. Hein, J. Phys. Condens. Matter 14 (2002) 13777] dealing with the analytical solution of the two-dimensional (2-D) Anderson localization problem due to disorder is generalized for anisotropic systems (two different hopping matrix elements in transverse directions). We discuss the mathematical nature of the metal–insulator phase transition which occurs in the 2-D case, in contrast to the 1-D case, where such a phase transition does not occur. In anisotropic systems two localization lengths arise instead of only one length.

WEAK LOCALIZATION EFFECTS IN METASTABLE SUPERSTRUCTURE NIOBIUM NITRIDE

Single-phase metastable α″-niobium nitride thin films have been synthesized on glass substrates by controlled reactive electron beam evaporation technique and are characterized by X-ray diffraction technique. The transport properties down to low temperatures have also been measured. The temperature dependence of resistivity has a minimum at 132 K and shows a remarkable change in the behavior below 25 K. These have been analyzed in the framework of weak localization effects. The analysis shows that the resistance minimum arises on account of three-dimensional weak localization and there is a cross-over to the two-dimensional weak localization regime at lower temperatures.

Electron transport in laterally confined phosphorusδlayers in silicon

Two-dimensional electron systems fabricated from a single layer of P-donors have been lithographically confined to nanometer scale in lateral directions. The electronic transport of such quasi-one-dimensional systems with and without a perpendicular magnetic field was characterized at cryogenic temperatures. Experimental data fit well with two-dimensional weak localization and interaction theory when the phase coherence length is shorter than the smaller dimension of the confinement. Below a transition temperature the wire conductance saturates.

Pressure-Induced Transition in Magnetoresistance of Single-Walled Carbon Nanotubes

We applied hydrostatic pressure (up to 10 GPa) to single-walled carbon nanotube bundles at low temperature (down to 2 K) to measure their magnetoresistance (MR) in a field up to 12 T. We found a pressure-induced transition in MR from positive to negative in the high-field regime. The onset of the transition occurs at approximately 1.5 GPa, which correlates closely with the tube shape transitions. The characteristics of the high-pressure MR are consistent with a model of pressure-induced two-dimensional weak localization.

2223: Usefulness of US-guided biopsy after digital mammographically guided two-dimensional localization for breast microcalcifications

2223: Usefulness of US-guided biopsy after digital mammographically guided two-dimensional localization for breast microcalcifications

Self-avoiding random walks and the two-dimensional localization theorem

We have addressed one of the most important and basic results in disordered systems, namely the complete localization of noninteracting electrons in two dimensions even at infinitesimal disorder. We present a proof of this assertion by combining some finer aspects of the behavior of self-avoiding random walks with Anderson's original approach to localization where a renormalized perturbation expansion of self-energy, whose terms have the self-avoiding random-walk character, was analyzed.

Study of single-walled carbon nanotube's differential conductance in high magnetic field under high pressure

Accompanied by the structural phase transition, the electron transport properties of single-walled carbon nanotubes bundles undergo a metal-semiconductor transition at a hydrostatic pressure of 1.5 GPa. In the semiconducting phase there coexist two effects——electron phase coherence which leads to two-dimensional electron weak localization, and Coulomb correlation which leads to the environmental quantum fluctuation of charge transport. We applied hydrostatic pressure up to 10 GPa to single-walled carbon nanotube bundles, and studied the bias voltage dependence of the differential conductance at low temperatures and in strong magnetic fields. Our results show that phase coherence and Coulomb correlation are two effects that independently influence on the electron transport process in the semiconducting phase of the single walled carbon nanotube bundles.

Logarithmic behavior of the conductivity of electron-beam deposited granularPt∕Cnanowires

We found that granular $\mathrm{Pt}∕\mathrm{C}$ composite nanowires have a logarithmic temperature dependence of conductivity in a wide range of temperatures. The logarithmic dependence can be explained by Coulomb interaction between Pt grains in a conductive carbon matrix. We stress the difference of the conductivity mechanism in the composite nanogranular material and known mechanisms in bulk metals/semiconductors and low-dimensional systems, including logarithmic dependence in systems with two-dimensional weak localization. Our observations show that local voltage fluctuations between grains result in the $\mathrm{log}(T)$ dependence for the samples with high conductivity (annealed nanowires), while the samples with low conductivity (as fabricated nanowires) appear to be insulators with a Coulomb gap.

Using a multilayer printed circuit board as position sensing electrode in a triple-GEM detector

The development of a triple-GEM imaging detector is reported. The triple-GEM detector provides two-dimensional (2-D) localization of ionizing events making use of a multilayer printed circuit board (X&Y anode) for position readout. Two-dimensional localization is achieved by associating one discrete delay line to each spatial coordinate. Results referring to differential nonlinearity (DNL), integral nonlinearity (INL) and spatial resolution are presented. The detector has been operated with Ar/Xe/CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (64/16/20) gas mixture at atmospheric pressure. 5.9 keV ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">55</sup> Fe source) photons were used to characterize the detector. The feasibility of the imaging technique is demonstrated and the major issues are addressed

Observation of Two-Dimensional Classical Wave Localization: Third Sound on SuperfluidHe4Films on a Disordered Substrate

We present the results of measurements of the propagation of third sound waves on superfluid 4He adsorbed to two-dimensional ordered and disordered substrates. In the disordered case we compare the experimental results to theoretical predictions of classical wave localization in such systems and conclude that classical wave localization is present in our system.

Study on wave localization in disordered periodic layered piezoelectric composite structures

The two-dimensional wave propagation and localization in disordered periodic layered 2-2 piezoelectric composite structures are studied by considering the mechanic-electric coupling. The transfer matrix between two consecutive sub-layers is obtained based on the continuity conditions. Regarding the variables of mechanical and electrical fields as the elements of the state vector, the expression of the localization factors in disordered periodic layered piezoelectric composite structures is derived. Numerical results are presented for two cases—disorder of the thickness of the polymers and disorder of the piezoelectric and elastic constants of the piezoelectric ceramics. The results show that due to the piezoelectric effects, the characteristics of the wave localization in disordered periodic layered piezoelectric composite structures are different from those in disordered periodic layered purely elastic ones. The wave localization is strengthened due to the piezoelectricity. And the larger the piezoelectric constant is, the larger the wave localization factors are. It is found that slight disorder in the piezoelectric or elastic constants of the piezoelectric ceramics can lead to more prominent localization phenomenon.

Weak localization effect in the strongly ferromagnetic Kondo compoundUCo0.5Sb2

Experimental results of the magnetization $(M)$, specific heat $({C}_{p})$, electrical resistivity $(\ensuremath{\rho})$, magnetoresistance (MR), and thermoelectric power $(S)$ are presented for single crystals of the tetragonal $\mathrm{U}{\mathrm{Co}}_{0.5}{\mathrm{Sb}}_{2}$ compound. Anomalies in the $M\mathit{(}T\mathit{)}$, $[{C}_{p}\mathit{(}T\mathit{)}]$, $\ensuremath{\rho}\mathit{(}T\mathit{)}$, $S\mathit{(}T\mathit{)}$ dependencies have allowed us to establish that $\mathrm{U}{\mathrm{Co}}_{0.5}{\mathrm{Sb}}_{2}$ undergoes a long-range ferromagnetic ordering at ${T}_{C}=64.5(2)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The temperature dependence of the magnetization measured fairly far below ${T}_{C}$ might be explained by considering both types of magnetic excitations: i.e., the spin-wave- and Stoner-type excitations. The $M\mathit{(}T\mathit{)}$ dependence is well represented by the relation $1\ensuremath{-}M(T)∕{M}_{s}=B{T}^{3∕2}+{B}_{1}{T}^{3∕2}\mathrm{exp}(\ensuremath{-}\mathrm{\ensuremath{\Delta}}∕T)$ with the determined spin-wave stiffness constant $D\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.2em}{0ex}}{\mathrm{\AA{}}}^{2}$ and a Stoner gap $\mathrm{\ensuremath{\Delta}}=69(2)\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The behavior of the electrical resistivity below about ${T}_{C}∕2$ is discussed in terms of the electron scattering on magnons with a dispersion relation ${E}_{q}=\mathrm{\ensuremath{\Delta}}+D{q}^{2}$ and the two-dimensional weak localization effect described by a \ensuremath{-}ln $T$ dependence. Negative magnetoresistance is observed over a wide range of temperatures below 150 K. The relative large field and temperature changes in the transverse MR around ${T}_{C}$ are thought to be due to the ferromagnetic order or/and damped critical fluctuations by the applied fields. Below 40 K the magnetoresistance behavior may be understood on the basis of the predominant elastic scattering predicted for two-dimensional systems with the weak localization effect. The thermoelectric power data indicate $\mathrm{U}{\mathrm{Co}}_{0.5}{\mathrm{Sb}}_{2}$ to be a $p$-type material with a moderate $S$ value of $\ensuremath{\sim}25\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{V}∕\mathrm{K}$ at room temperature. The ${T}^{3∕2}$ dependence observed in the $S\mathit{(}T\mathit{)}$ curves for $T\ensuremath{\leqslant}30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is consistent with the electron-magnon scattering process. The high anisotropy and temperature dependence of the $S\mathit{(}T\mathit{)}$ curves may be explained by adopting a phenomenological model for a Kondo lattice.

Spin–Orbit Interaction and Two-Dimensional Weak Localization in a Carbon Matrix with Cobalt Nanoclusters

The magnetic-field dependence of the magnetoresistive effect in carbon fibers that contain cobalt nanoclusters and exhibit effects of weak localization at low temperatures (T < 45 K) is investigated on the metal side of the dielectric-metal transition. The carbon fibers are prepared by heat treatment of carboxylated cellulose after the substitution of cobalt cations for protons of COOH groups. It is found that, under conditions of two-dimensional weak localization at temperatures below 10 K, the carbon fibers possess an alternating magnetoresistance due to spin-orbit scattering of electrons by cobalt nanoclusters. The time of phase breaking of the wave function and the time of spin-orbit scattering are determined from a comparison of the experimental and theoretical magnetic-field dependences of the electrical resistance.

Contribution of head shadow and pinna cues to chronic monaural sound localization.

Monaurally deaf people lack the binaural acoustic difference cues in sound level and timing that are needed to encode sound location in the horizontal plane (azimuth). It has been proposed that these people therefore rely on spectral pinna cues of their normal ear to localize sounds. However, the acoustic head-shadow effect (HSE) might also serve as an azimuth cue, despite its ambiguity when absolute sound levels are unknown. Here, we assess the contribution of either cue in the monaural deaf to two-dimensional (2D) sound localization. In a localization test with randomly interleaved sound levels, we show that all monaurally deaf listeners relied heavily on the HSE, whereas binaural control listeners ignore this cue. However, some monaural listeners responded partly to actual sound-source azimuth, regardless of sound level. We show that these listeners extracted azimuth information from their pinna cues. The better monaural listeners were able to localize azimuth on the basis of spectral cues, the better their ability to also localize sound-source elevation. In a subsequent localization experiment with one fixed sound level, monaural listeners rapidly adopted a strategy on the basis of the HSE. We conclude that monaural spectral cues are not sufficient for adequate 2D sound localization under unfamiliar acoustic conditions. Thus, monaural listeners strongly rely on the ambiguous HSE, which may help them to cope with familiar acoustic environments.

Bridging multi-scale method for localization problems

A bridging multi-scale method is proposed for the analysis of a class of localization problems in which the micropolar-continuum model is used to describe the localized deformation and the dynamic failure occurs only in a small number of localized regions. It starts with a concurrent discretization of the entire domain with both coarse- and fine-scale finite-element meshes. The coarse-scale mesh is employed to capture the nonlinear response with long wavelength outside the localized regions, whereas the fine-scale mesh captures the detailed physics of the localized deformation. For both the coarse and fine-scale meshes to coexist, a bridging scale term is constructed so that the information common to both scales is correctly subtracted. To achieve computational efficiency, the localized regions are first identified by a preliminary calculation and the fine-scale degrees of freedom (DOFs) outside the localized regions are mathematically represented by the construction of dynamic interface conditions applied to the edges of these regions. Hence, a large portion of the fine-scale DOFs are eliminated and the fine-scale equations are reduced to a much smaller set with the added dynamic interface conditions. The two-way coupled coarse-scale and reduced fine-scale equations are then solved by a mixed time integration procedure. Applications to one-dimensional and two-dimensional dynamic shear localization problems are presented.

Electronic Transport Properties of IncipientGraphitic Domains Formation in PAN Derived Carbon Nanofibers

The carbon nanofibers used in this work were derived from a polyacrylonitrile (PAN)/N, N-dimethyl formamide (DMF) precursor solution using electrospinning and vacuum pyrolysis techniques. Their conductivity, /spl sigma/, was measured at temperatures between 1.9 and 300 K and transverse magnetic field between -9 and 9 T. Zero magnetic field conductivity /spl sigma/(0,T) was found to increase monotonically with the temperature with a convex /spl sigma/(0,T) versus T curve. Conductivity increases with the external transverse magnetic field, revealing a negative magnetoresistance at temperatures between 1.9 and 10 K, with a maximum magnetoresistance of -75 % at 1.9 K and 9 T. The magnetic field dependence of the conductivity and the temperature dependence of the zero-field conductivity are best described using the two-dimensional weak localization effect.

Comment on ‘Exact analytical solution for the generalized Lyapunov exponent of thetwo-dimensional Anderson localization’

In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announcedan analytical solution of the two-dimensional Anderson localization problem via thecalculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certainenergies and small disorder strength they observed delocalized states. We study thetransmission properties of the same model using well-known transfer matrix methods.Our results disagree with the findings obtained using signal theory. We pointto the possible origin of this discrepancy and comment on the general strategyof using a generalized Lyapunov exponent for studying Anderson localization.

Reply to Comment on ‘Exact analytical solution for the generalized Lyapunov exponent ofthe two-dimensional Anderson localization’

We reply to comments by Markoš et al (2004 J. Phys.: Condens. Matter 16) on our recent paper(Kuzovkov et al 2002 J. Phys.: Condens. Matter 63 13777). We demonstrate that our quitedifferent viewpoints stem for the different physical assumptions made prior to the choiceof the mathematical formalism. The authors of the comment expect a priori tosee a single thermodynamic phase while our approach is capable of detectingthe co-existence of distinct pure phases. The limitations of the transfer matrixtechniques for the multi-dimensional Anderson localization problem are discussed.

Two-dimensional localization of a phantom sound image controlled by the level differences among four loudspeakers in a vertical plane facing a listener

Two-dimensional localization of a phantom sound image controlled by the level differences among four loudspeakers in a vertical plane facing a listener

Weak-field magnetoresistance anomaly and Shubnikov–de Haas oscillations in Sn-doped InSb thin films on GaAs (100) substrates

Distinctive magnetoresistance (MR) effects in weak magnetic fields before the appearance of Shubnikov–de Haas (SdH) oscillations at low temperatures in Sn-doped (7×10 16 cm −3) InSb films grown on GaAs(100) substrates by MBE have been investigated with decreasing film thickness d from 1 μm . The negative MR found in weak magnetic fields for d⩾0.5 μm can be broadly divided into two regimes: T-sensitive negative MR below B c observed with anisotropy between parallel and perpendicular magnetic field and a T-insensitive parabolic one above B c observable only under in-plane magnetic fields. The latter is ascribable to the skipping orbit effect due to surface boundary scattering. In vanishing magnetic fields far below B c, the negative MR reduces with decreasing d and the different positive MR overlaps with it below 0.5 μm , eventually dominating the positive MR at d∼0.2 μm . These results have been analyzed using a two-layer model for the films, where the composition of the upper layer under the surface and the lower one adjacent to the InSb/GaAs interface is assumed. The MR data in the extremely weak magnetic fields below 100 G for each layer have been successfully fitted to the two-dimensional (2D) weak localization (WL) theory. These results explain that the crossover from the 2D WL to the weak anti-localization (WAL) occurs when the interface is approached with the increase of SO interaction in the layers caused by the increased influence of the asymmetric potential at the hetero interface (Rashba term) and the SO rate in the intrinsic InSb film due to the crystal field of the zinc-blende structure (Dresselhaus term) is as small as τ so −1⩽3×10 8 s −1 .