2D Fluctuations Research Articles

Surface Charge Density Wave Phase Transition inNbSe3

The two charge-density wave (CDW) transitions in NbSe3 were investigated by scanning tunneling microscopy (STM) on an in situ cleaved (b, c) plane. The temperature dependence of first-order CDW satellite spots, obtained from the Fourier transform of the STM images, was measured between 5 and 140 K to extract the surface critical temperatures (T{s}). The low-T CDW transition occurs at T{2s}=70-75 K, more than 15 K above the bulk T{2b}=59 K while at exactly the same wave number. A plausible mechanism for such an unusually high surface enhancement is a softening of transverse phonon modes involved in the CDW formation. The regime of 2D fluctuations is analyzed according to a Berezinskii-Kosterlitz-Thouless type of surface transition, expected for this incommensurate 2D CDW, by extracting the temperature dependence of the order parameter correlation functions.

Different regions of fluctuation conductivity in Sn-doped Cu 0.5Tl 0.5Ba 2Ca 2Cu 3−ySn yO 10−δ superconductors

Fluctuation induced conductivity of Cu 0.5Tl 0.5Ba 2Ca 2Cu 3− y Sn y O 10−δ superconductors have been studied from the resistivity vs. temperature data. The logarithmic plots of excess conductivity (Δ σ) vs. reduced temperatures [ ε = ( T − T c mf ) / T c mf ] show two crossover temperatures with three exponents. A distinct cross-over from two-dimensional to three-dimensional conductivity in accordance with the 2D, 3D Aslamazov–Larkin equations have been observed in all the samples. Another cross over from 2D to 0D fluctuations has also been witnessed. The FIC data fits well with 3D, 2D and 0D fluctuations for lower Sn doping, while it deviates considerably for higher Sn concentration. Also the FIC analysis shows the deterioration in quality of samples (increased Δ T c), increase in anisotropy and decrease in inter-layer coupling strength J with increased Sn content. These factors might be contributing to the suppression of T c in these samples.

Two-Dimensional Spin Dynamics in the Itinerant Ferromagnet LaCoPO Revealed by Magnetization and 31P-NMR Measurements

We have performed magnetization and $^{31}$P-NMR measurements on the itinerant ferromagnet LaCoPO (Curie temperature $T_{\rm Curie}\sim 44$ K) with a layered structure in order to investigate spin dynamics in the paramagnetic state. The linear scaling between the Knight shift $K$ at the P site and the bulk susceptibility $\chi$ above $T_{\rm Curie}$ indicates that the P nucleus is suitable for investigating magnetic properties. The temperature and magnetic field dependences of the nuclear spin-lattice relaxation rate divided by the temperature $1/T_1T$ at the P site show characteristic features of itinerant ferromagnets, such as ZrZn$_2$ and Y(Co$_{1-x}$Al$_x$)$_2$. In addition, the relationship between $1/T_1T$ and $\chi$ above $T_{\rm Curie}$ suggests that ferromagnetic fluctuations possess a two-dimensional (2D) characteristic. The present data show that LaCoPO is a unique ferromagnet, where the 2D fluctuations anticipated from the crystal structure are predominant down to almost $T_{\rm Curie}$.

When do particles follow field lines?

We examine charged particle transport perpendicular to the large scale magnetic field. We find that the limit of an infinite parallel mean free path of particles diffusing along the large scale magnetic field is a necessary condition for which the diffusive spread of the magnetic field lines leads to a proportional spread of the particles. When it occurs this requires that parallel mean free path is well in excess of the smaller of the system size and the turbulence ultrascale. However, there are alternative situations in which particles may diffuse, but field lines do not. In the latter cases the asymptotic behavior is that which persists after the parallel mean free path exceeds some multiple of the correlation scales. This phenomenon of diffusing particles/non‐diffusing field lines is typically determined by the 2D turbulence spectrum, where the diffusion coefficient of the magnetic field due to 2D turbulence can diverge if the spectrum of the 2D fluctuations is not well behaved at small wave numbers. We also show that the classical relation between parallel and perpendicular diffusion for high energy particles is consistent with the field line random walk description of particle diffusion.

Perpendicular Transport of Energetic Charged Particles in Nonaxisymmetric Two‐Component Magnetic Turbulence

We examine energetic charged particle diffusion perpendicular to a mean magnetic field B0 due to turbulent fluctuations in a plasma, relaxing the common assumption of axisymmetry around B0 and varying the ratio of two fluctuation components, a slab component with parallel wavenumbers and a two-dimensional (2D) component with perpendicular wavenumbers. We perform computer simulations mostly for 80% 2D and 20% slab energy and a fluctuation amplitude on the order of B0. The nonlinear guiding center (NLGC) theory provides a reasonable description of asymptotic perpendicular diffusion as a function of the nonaxisymmetry and particle energy. These values areroughlyproportionaltotheparticlespeedtimesthefieldlinediffusioncoefficient,withaprefactorthatismuchlower than in the classical field line random walk model of particle diffusion. NLGC predicts a prefactor in closer agreement with simulations. Next we consider extreme fluctuation anisotropy and the approach to reduced dimensionality. For 99% slab fluctuation energy, field line trajectories are diffusive, but the particle motion is subdiffusive. For 99% 2D fluctuation energy, both field lines and particle motions are initially subdiffusive and then diffusive, but NLGC gives unreliable results. The time dependence of the running particle diffusion coefficient shows that in all cases asymptotic diffusionisprecededbyfreestreamingandsubdiffusion,but thelatterdiffersfromstandardcompoundsubdiffusion.We can model the time profiles in terms of a decaying negative correlation of the perpendicular velocity due to the possibility of backtracking along magnetic field lines.

Excess conductivity of Cu0.5Tl0.5Ba2Ca1Cu2O8−δ thin films induced by thermal fluctuation: importance of 3D fluctuations

The superconductivity in Cu0.5Tl0.5Ba2Ca1Cu2O8−δ (Cu0.5Tl0.5-1212) thin films is studied in the light of the Aslamazov–Larkin (AL) theoryof fluctuation-induced conductivity (FIC). Analysis of FIC has shown thatremoval/addition of oxygen in the charge reservoir layer after post-annealing ofCu0.5Tl0.5-1212 thin films changes the dimensionality of the fluctuations which induce conductivityof mobile carriers. The samples post-annealed in nitrogen have shown higherTc(0) with3D behavior of FIC over a wide temperature range, whereas the samples post-annealed in oxygen havesmaller Tc(0) and possess only 2D fluctuations. These results suggest that the value ofTc(0) also depends on the dimensionality of thermal fluctuations which induce excessconductivity.

Micromachined Linear Brownian Motor: A Nanosystem Exploting Brownian Motion of Nanobeads for Uni-directional Transport

AbstractNanosystems operating in liquid media may suffer from random thermal fluctuations. Some natural nanosystems, e.g. biomolecular motors, which survive in an environment where the energy required for bio-processes is comparable to thermal energy, exploit these random fluctuations to generate a controllable unidirectional movement. Inspired by the nature, a transportation system of nanobeads achieved by exploiting Brownian motion were proposed and realized. This decreases energy consumption and saves the energy compared to ordinal pure electric or magnetic drive. In this paper we present a linear Brownian motor with a 3-phase electrostatic rectification aimed for unidirectional transport of nanobeads in microfluidic channels. The transport of the beads is performed in 1 μm deep, 2 μm wide PDMS microchannels, which constrain three-dimensional random motion of nanobeads into 1D fluctuation, so-called tamed Brownian motion. We have experimentally traced the rectified motion of nanobeads and observed the shift in the beam distribution as a function of applied voltage. The detailed computational analysis on the importance of switching sequence on the speed performance of motor is performed and compared with the experimental results showing a good agreement.

2D and 3D Turbulent Fluctuations in Open Channel Flow with Re τ = 590 Studied by Large Eddy Simulation

Well-resolved 3D Large Eddy Simulations (LES) are presented for open channel flow at a Reynolds number Reτ = 590 based on friction velocity uτ and water depth h. The results are depth-averaged and thereby information is obtained on the 2D horizontal fluctuations in the channel. The total turbulence is decomposed into 2D and 3D fluctuations and the energy content of these as well as their spectral distribution is studied. It is found that only 15% of the fluctuating energy is contained in the 2D fluctuations and that these are mostly of scales larger than the water depth while the 3D fluctuations are restricted by the limited vertical extent of the water body and have scales smaller than the water depth. Information is obtained on the dispersion terms arising from the depth-averaging procedure, and scalar transport due to a vertical line source of tracer is studied thereby investigating the contribution of the 2D and 3D fluctuations to the transverse mixing of the scalar.

Trapping and Diffusive Escape of Field Lines in Two‐Component Magnetic Turbulence

Recent studies have shown that transport along magnetic field lines in turbulent plasmas admits a surprising degree of persistent trapping due to small-scale topological structures. This underlies the partial filamentation of magnetic connection from small regions of the solar corona to Earth orbit, as indicated by the observed dropouts (i.e., inhomogeneity and sharp gradients) of solar energetic particles. We explain the persistence of such topological trapping using a two-component model of magnetic turbulence with slab and two-dimensional (2D) fluctuations, which has provided a useful description of transport phenomena in the solar wind. In the presence of slab turbulence, the diffusive escape of field lines from 2D orbits is suppressed by either a strong or an irregular 2D field. For slab turbulence superposed on a 2D field with a single, circular island, we present an analytic theory, confirmed by numerical simulations, for the trapping length and its dependence on various parameters. For a turbulent 2D+slab field, we find that the filamentation of magnetic connectivity to the source is sharply delineated by local trapping boundaries, defined by a local maximum in the mean squared field along the 2D orbit, because of a similar suppression effect. We provide a quasi-linear theory for field-line diffusion in a turbulent 2D+slab field, which indicates that irregularity of the 2D orbit enhances the suppression of slab diffusion. The theory is confirmed by computer simulations. These concepts provide a physical explanation of the persistence and sharpness of dropouts of solar energetic particles at Earth orbit.

Role of Interchain Hopping in the Magnetic Susceptibility of Quasi-One-Dimensional Electron Systems

The role of interchain hopping in quasi-one-dimensional (Q-1D) electron systems is investigated by extending the Kadanoff-Wilson renormalization group of one-dimensional (1D) systems to Q-1D systems. This scheme is applied to the extended Hubbard model to calculate the temperature ($T$) dependence of the magnetic susceptibility, $\chi (T)$. The calculation is performed by taking into account not only the logarithmic Cooper and Peierls channels, but also the non-logarithmic Landau and finite momentum Cooper channels, which give relevant contributions to the uniform response at finite temperatures. It is shown that the interchain hopping, $t_\perp$, reduces $\chi (T)$ at low temperatures, while it enhances $\chi(T)$ at high temperatures. This notable $t_\perp$ dependence is ascribed to the fact that $t_\perp$ enhances the antiferromagnetic spin fluctuation at low temperatures, while it suppresses the 1D fluctuation at high temperatures. The result is at variance with the random-phase-approximation approach, which predicts an enhancement of $\chi (T)$ by $t_\perp$ over the whole temperature range. The influence of both the long-range repulsion and the nesting deviations on $\chi (T)$ is further investigated. We discuss the present results in connection with the data of $\chi (T)$ in the (TMTTF)$_2X$ and (TMTSF)$_2X$ series of Q-1D organic conductors, and propose a theoretical prediction for the effect of pressure on magnetic susceptibility.

Real‐space visualization of the phase transition of the In/Si(111) system

AbstractLow‐energy electron diffraction and scanning tunneling microscopy (STM) were used to investigate the temperature‐induced phase transition of a room‐temperature 4 × 1 (4 × 1‐RT) phase of the In/Si(111) surface to a low‐temperature 8 × 2 (8 × 2‐LT) phase. Upon cooling, dark, one‐dimensional (1D) stripes appear inhomogeneously within the 4 × 1‐RT phase at temperatures above a transition temperature (Tc), coalesce to form two‐dimensional (2D) islands, and the overall surface finally transforms into the 8 × 2‐LT phase below Tc. The local current–voltage spectroscopy reveals that the dark 1D stripes inherit the nature of the low‐temperature phase, distinguishing it from the defect‐induced period‐doubling modulations. The fluctuations of the 1D stripes are observed in successive STM images. The presence of defects suppresses the 1D fluctuations, while it is obstructive to the 2D condensation of the LT phase below Tc. Copyright © 2006 John Wiley & Sons, Ltd.

Conductivity fluctuation of YBa2Cu3O7 - delta/Sr2YSbO6/SrTiO3 thin films

Thermal fluctuations in the electric conductivity of YBa2Cu3O7 - delta superconducting thin films grown on Sr2YSbO6 novel substrate materials in the film form were experimentally studied. YBa2Cu3O7 - delta films were grown by using a dc-technique on Sr2YSbO6 substrates, which were produced by rf magnetron sputtering. X-ray diffraction analysis evidenced that the Sr2YSbO6 films grow on conventional SrTiO3 substrates in a preferential orientation along the (100) planes direction with lattice parameter a=4,43() Å. The YBa2Cu3O7 - delta thin films, grown on Sr2YSbO6 films, exhibit an oriented growth in the (001) crystallographic direction, with lattice constant c=11,65(9) Å. Morphological characterizations were performed by means atomic force microscopy. Experiments of electrical resistivity show that the YBa2Cu3O7 - delta films present a normal-superconducting transition with critical temperature Tc=82,33 K. Fluctuation analysis for the YBa2Cu3O7 - delta thin films were performed by utilizing the concept of logarithmic derivative of the conductivity excess. Above the critical temperature Tc we experimentally determine the occurrence of Gaussian 3D, 2D and fractal fluctuation regimes. A genuinely critical region identified by the exponent lambdaCR=0,35 were obtained close to Tc. This critical regime is effectively described by the 3D-XY model.

Finite-Temperature Charge-Ordering Transition and Fluctuation Effects in Quasi One-Dimensional Electron Systems at Quarter Filling

Finite-temperature charge-ordering phase transition in quasi one-dimensional (1D) molecular conductors is investigated theoretically, based on a quasi 1D extended Hubbard model at quarter filling with interchain Coulomb repulsion $V_\perp$. The interchain term is treated within mean-field approximation whereas the 1D fluctuations in the chains are fully taken into account by the bosonization theory. Three regions are found depending on how the charge ordered state appears at finite temperature when $V_\perp$ is introduced: (i) weak-coupling region where the system transforms from a metal to a charge ordered insulator with finite transition temperature at a finite critical value of $V_\perp$, (ii) an intermediate region where this transition occurs by infinitesimal $V_\perp$ due to the stability of inherent 1D fluctuation, and (iii) strong-coupling region where the charge ordered state is realized already in the purely 1D case, of which the transition temperature becomes finite with infinitesimal $V_\perp$. Analytical formula for the $V_\perp$ dependence of the transition temperature is derived for each region.

Plasma mixing as a cause of solar wind magnetic field variations

In the present paper, we have studied the effect of plasma mixing on the small-scale field configurations. We have employed theoretical models and numerical simulations to describe magnetic field structures formed by the mixing motion of the interplanetary plasma. The small-scale magnetic fluctuations share properties with waves and with turbulence as well. It is shown that plasma mixing can account for both wave-like and turbulence-like behavior. Mixing can also explain the formation and the dominance of the so-called 2D fluctuations. Four-point measurements provide a new tool for the experimental investigation of the field configurations. Our effort was to identify the effect of plasma mixing. In a slow laminar mixing flow sheet-like structures are formed everywhere in the plasma. The existence of these kind of structures has been tested using the magnetometer data of the four Cluster spacecraft. Our results suggest that plasma mixing plays a significant role in the formation of the small-scale magnetic fluctuations of the solar wind. Our results support that the 2D component dominates the magnetic fluctuations.

Description of magnetic short-range order in the 2D Heisenberg model: Auxiliary fermions with reduced self-consistency

Critical magnetic fluctuations in the two-dimensional spin 1 2 quantum Heisenberg antiferromagnet (QHAF) are studied at low temperature. Spin operators are represented by fermions, and the local constraint onto the physical subspace is treated approximately as a global one. The 2D fluctuations have to be treated self-consistently beyond mean field. We propose and compare two appropriate schemes: the first one is analogous to the well-known FLEX, based on self-consistent fermion propagators, the other avoids renormalising the (unphysical) fermion, while retaining the magnetic susceptibility a self-consistent quantity. Both reproduce the correlation length ξ ( T ) ∼ exp ( a J / T ) and the critical slowing down, but only the latter, ‘minimal’ self-consistent approximation (MSCA) yields propagating spin-wave like modes, characteristic of short-range order at length scales < ξ .

Low-dimensional ordering and fluctuations in methanol-β-hydroquinone clathrate studied by x-ray and neutron diffraction

Methanol-$\ensuremath{\beta}$-hydroquinone clathrate has been established as a model system for dielectric ordering and fluctuations and is conceptually close to magnetic spin systems. In x-ray and neutron diffraction experiments, we investigated the ordered structure, the one-dimensional (1D) and the three-dimensional critical scattering in the paraelectric phase, and the temperature dependence of the lattice constants. Our results can be explained by microscopic models of the methanol pseudospin in the hydroquinone cage network, in consistency with previous dielectric investigations. A coupling of the 1D fluctuations to local strains leads to an anomalous temperature dependence of the 1D lattice parameter in the paraelectric regime.

Vortex phases in modulation-free (Bi,Pb)-2212 crystals

We have investigated the vortex phase diagrams of modulation-free Bi 1.7Pb 0.4Sr 2Ca 0.9Cu 2O 8 crystals and Pb-free Bi 2Sr 2CaCu 2O 8+ δ crystals. In (Bi,Pb)-2212 crystals, the strongly reduced anisotropy as well as the presence of a significant amount of disorder induce important differences compared to Bi-2212 crystals. We have probed the activation energies of the vortices by means of magnetic relaxation measurements, both above and below the second-magnetization peak. In the vortex phase below the peak, a power law dependence U ∝ (1/ j) μ is found, with an exponent μ = 0.54 which compares favorably with the Bragg Glass prediction. In the disordered phase situated above the second-magnetization peak line, the barriers are found to slowly diverge as U ∝ ln(1/ j). This suggests the existence of a glassy state in this region of the phase diagram. We have carefully measured the onset of the irreversibility in the disordered phase in both crystals. Above the 2D–3D crossover field H cr, the resulting irreversibility lines are shown to be qualitatively described using a Lindemann approach in a 2D fluctuation regime.

Growth, structure, and superconducting properties of Bi2Sr2Ca2Cu3O10 and (Bi,Pb)2Sr2Ca2Cu3O10‐y crystals

AbstractLarge and high‐quality single crystals of both Pb‐free and Pb‐doped high temperature superconducting compounds (Bi1‐xPbx)2Sr2Ca2Cu3O10‐y (x = 0 and 0.3) were grown by means of a newly developed “Vapour‐Assisted Travelling Floating Zone” technique (VA‐TSFZ). This modified zone‐melting technique was realised in an image furnace and allowed for the first time to grow Pb‐doped crystals by compensating for the Pb losses occurring at high temperature. Crystals up to 3×2×0.1 mm3 were successfully grown. Post‐annealing under high pressure of O2 (up to 10 MPa at T = 500°C) was undertaken to enhance Tc and improve the homogeneity of the crystals. Structural characterisation was performed by single‐crystal X‐ray diffraction (XRD) and the structure of the 3‐layer Bi‐based superconducting compound was refined for the first time. Structure refinement showed an incommensurate superlattice in the Pb‐free crystals. The space group is orthorhombic, A2aa, with cell parameters a = 27.105(4) Å, b = 5.4133(6) Å and c = 37.009(7) Å. Superconducting studies were carried out by A.C. and D.C. magnetic measurements. Very sharp superconducting transitions were obtained in both kinds of crystals (ΔTc ≤ 1 K). In optimally doped Pb‐free crystals, critical temperatures up to 111 K were measured. Magnetic critical current densities of 2�105 A/cm2 were measured at T = 30 K and μ0H = 0 T. A weak second peak in the magnetisation loops was observed in the temperature range 40‐50 K above which the vortex lattice becomes entangled. We have measured a portion of the irreversibility line (0.1‐5 Tesla) and fitted the expression for the melting of a vortex glass in a 2D fluctuation regime to the experimental data. Measurements of the lower critical field allowed to obtain the dependence of the penetration depth on temperature: the linear dependence of λ(T) for T &lt; 30 K is consistent with d‐wave superconductivity in Bi‐2223. (© 2004 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Novel properties of 0.4 nm single-walled carbon nanotubes templated in the channels ofAlPO4-5single crystals

We review our experimental and theoretical studies on the ultra-smallsingle-walled carbon nanotubes (SWNTs) fabricated in the 1 nm channels ofAlPO4-5(AFI) zeolite single crystals. The structure of the SWNT was characterized by transmissionelectron microscopy (TEM), diffuse x-ray diffraction, and micro-Raman measurements, allconsistently indicating a diameter of 0.4 nm, at or close to the theoretical limit. The largecurvature in the 0.4 nm SWNTs makes the nanotubes marginally stable. On the one hand,the free-standing 0.4 nm SWNTs can be thermally destroyed at a much lower temperaturethan larger sized SWNTs but, on the other hand, it introduces a variety of interestingmaterial characteristics such as the large split of the G-like Raman modes, softeningof the radial breathing modes, closing of the semiconducting gap so that the(5,0) nanotubes are metallic, and the enhancement of the electron–phonon coupling that makesthese ultra-small nanotubes superconducting at a relatively high temperature (15 K). Bandstructure and dielectric function of the 0.4 nm SWNTs were calculated using thelocal-density-functional approach. The calculated dielectric functions yield predictions invery good agreement with the experimentally measured absorption spectra. Theabsorption bands can be identified as dipole transitions between states in thevicinity of the van Hove singularities. Further confirmation of these dipole-allowedtransitions was obtained by the resonant Raman excitation spectrum. Electrictransport measurements were conducted on the SWNT@AFI crystals. As the zeolitematrix is insulating, electric conduction can be ascribed to the nanotubes. It wasshown that the conductivity of the 0.4 nm SWNTs is governed by a 1D electronhopping process at temperatures above 20 K. The measured magnetic and transportproperties revealed that at temperatures below 20 K, these ultra-small SWNTsexhibit superconducting behaviour with a mean-field superconducting transitiontemperature of 15 K. The superconducting characteristics display smooth temperaturevariations owing to 1D fluctuation. The observed anisotropic Meissner effect, thesuperconducting gap and fluctuation supercurrent were consistently explainedon the basis of the Ginzburg–Landau formalism. By means of lithium doping,the electronic structure of the ultra-small SWNTs can be modified. Results ofa first-principles calculation as well as experimental observation show that theSWNT@AFI system can adsorb lithium atoms up to a density as high as 10 wt%.

One-dimensional instability in BaVS3.

The 3d(1) system BaVS3 undergoes a series of remarkable electronic phase transitions. We show that the metal-insulator transition at T(MI)=70 K is associated with a structural transition announced by a huge regime of one-dimensional (1D) lattice fluctuations, detected up to 170 K. These 1D fluctuations correspond to a 2k(F)=c(*)/2 charge-density wave (CDW) instability of the d(z(2)) electron gas. We discuss the formation below T(MI) of an unconventional CDW state involving the condensation of the other V4+ 3d(1) electrons of the quasidegenerate e(t(2g)) orbitals. This study stresses the role of the orbital degrees of freedom in the physics of BaVS3 and reveals the inadequacy of current first principle band calculations to describe its electronic ground state.