Theory of Decay of Superfluid Turbulence in the Low-Temperature Limit

We review the theory of relaxational kinetics of superfluid turbulence—a tangle of quantized vortex lines—in the limit of very low temperatures when the motion of vortices is conservative. While certain important aspects of the decay kinetics depend on whether the tangle is non-structured, like the one corresponding to the Kibble-Zurek picture, or essentially polarized, like the one that emulates the Richardson-Kolmogorov regime of classical turbulence, there are common fundamental features. In both cases, there exists an asymptotic range in the wavenumber space where the energy flux is supported by the cascade of Kelvin waves (kelvons)—precessing distortions propagating along the vortex filaments. At large enough wavenumbers, the Kelvin-wave cascade is supported by three-kelvon elastic scattering. At zero temperature, the dissipative cutoff of the Kelvin-wave cascade is due to the emission of phonons, in which an elementary process converts two kelvons with almost opposite momenta into one bulk phonon. Along with the standard set of conservation laws, a crucial role in the theory of low-temperature vortex dynamics is played by the fact of integrability of the local induction approximation (LIA) controlled by the parameter Λ=ln?(λ/a ₀), with λ the characteristic kelvon wavelength and a ₀ the vortex core radius. While excluding a straightforward onset of the pure three-kelvon cascade, the integrability of LIA does not plug the cascade because of the natural availability of the kinetic channels associated with vortex line reconnections. We argue that the crossover from Richardson-Kolmogorov to the Kelvin-wave cascade is due to eventual dominance of local induction of a single line over the collective induction of polarized eddies, which causes the breakdown of classical-fluid regime and gives rise to a reconnection-driven inertial range.     

Homogeneous Turbulence in Superfluid 4He in the Low-Temperature Limit: Experimental Progress

Selected advances in the research on the dynamics of tangles of quantized vortices in superfluid helium with little normal component during the last 50 years are briefly reviewed. The main emphasis is on the experimental techniques of generating and probing homogeneous one-component superfluid turbulence of various energy spectra in superfluid ⁴He in the low-temperature limit. The most recent experimental progress, modern theoretical concepts and future outlook are summarized.     

Superfluid 3He Confined to a Single 0.6 Micron Slab Stability and Properties of the A-Like Phase Near the Weak Coupling Limit

We present the first study of the phase diagram of a thick film of superfluid ³He confined within a nanofabricated slab geometry. This cryogenic microfluidic chamber provides a well-defined environment for the superfluid, in which both the regular geometry and surface roughness may be fully characterised. The chamber is designed with a slab thickness d=0.6 μm and 3 mm thick walls to allow pressure tuning of the effective confinement between 0 and 5.5 bar. Over this range the zero temperature superfluid coherence length, ξ₀, decreases by approximately a factor of two from 77 to 40 nm. Samples have so far been cooled to 350 μK. We use nuclear magnetic resonance (NMR) to ‘finger-print’ the superfluid order parameter, with the static field applied perpendicular to the slab. To enable us to resolve high quality NMR signals from the tiny amount of superfluid ³He in the slab, we have developed a spectrometer using a two stage SQUID amplifier with unprecedented sensitivity. Simple NMR zeugmatography allows the slab signal to be unambiguously distinguished from that of a small bulk liquid region near the fill line. The measured slab transition temperature, T _c ^slab , shows a suppression proportional to ξ ₀ ² , as expected theoretically, but the absolute suppression is less than expected. Below T _c ^slab , an A-like phase is stable over a significant temperature range. A transition temperature, T _AX , is measured on warming from a so far unidentified phase, occurring at lower temperatures, into the A-phase. At the pressures investigated (3 to 5.5 bar) the transition appears to occur at an approximately fixed value of the effective confinement d/ξ(T _AX ). In this geometry we predict that the A-phase will be stable to T=0 at zero pressure.     

Interaction between gallium atoms and the inner walls of single-walled carbon nanotubes

The interaction between individual Ga atoms and the inner walls of both (8, 8) and (12, 0) carbon nanotubes (CNTs) is investigated using first principles calculations based on the density functional theory. We find that a single Ga atom favorably adsorbs at the center site (H) of a hexagonal ring and diffuses on the inner wall of a perfect CNT with very low energy barriers. In the case of CNTs containing monovacancies, a single Ga?atom can heal the topological structure of a monovacancy in a (8, 8) CNT but not in a (12, 0) CNT. Our calculations show that the Ga atom adsorbed at the monovacancy in the CNT can alter the electronic structure of the tube significantly.     

Non-linear Localized Lattice Mode Coupling Mechanism and the Pseudogap in High-temperature Superconducting Cuprates

The pseudo-gap phenomena in high-temperature cuprate superconductors is an outstanding puzzle with no consensus yet on its physical origin. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors is re-examined to investigate whether unusual lattice mechanisms could cause a pseudo-gap. By assuming an electron predominantly interacting with a non-linear Q ₂ mode of the oxygen clusters in the CuO₂ planes, we show that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. We show that the polaron formation by the non-linear mode can cause a pseudo-gap of d-wave symmetry before the onset of coherence in the superconducting pairing. We suggest a simple phenomenological explanation of the pseudo-gap crossover temperature and the Fermi arcs. The discussion may be relevant for the pseudo-gap in non-superconducting giant magnetoresistive manganites.     

Anomalous Resistivity and the Electron–Polaron Effect in the Two-Band Hubbard Model with One Narrow Band

We search for anomalous normal and superconductive behavior in the two-band Hubbard model with one narrow band. We analyze the influence of the electron?Cpolaron effect and the Altshuler?CAronov effect on effective mass enhancement and scattering times of heavy and light components in the clean case. We find anomalous behavior of resistivity at high temperatures $T > W_{h}^{*}$ both in 3D and 2D situations. The SC instability in the model is governed by an enhanced Kohn?CLuttinger effect for p-wave pairing of heavy electrons via polarization of light electrons.     

Spectral Properties of a Doped Antiferromagnet with Pairing Correlations

In this paper, we study the spectral properties of a phenomenological model for a weakly doped antiferromagnet. In this model, it is assumed that each carrier moves in one of the two sublattices where it was introduced. Such a situation corresponds to a case of underdoped high-temperature superconductors with the free carrier spectra maximum at k=(±π/2,±π/2) and with a four-pocket Fermi surface. We study the spectral properties of the model by taking into account both the fluctuations of the phases of the superconducting order parameter and spins of the antiferromagnetic background. It is shown that the hole spectral function and the density of states are strongly affected by these fluctuations. In particular, we argue that these fluctuations can be responsible for the temperature evolution of the Fermi pockets in cuprate superconductors.     

Calculation of the Free Energy of Fullerenes in the Gross–Neveu Model

Methods of field theory on Riemannian manifolds were used to study the Gross–Neveu model (incorporating the Hubbard model as a special case) at T 0. The generating functional of the Gross–Neveu model on a torus, S ² _r S ¹ , was obtained by the functional integration method. The model was regularized using the theory of zeta functions. Double sums were calculated using recurrent formulas. For the zeta function of the Dirac operator in the limit of s = 1, we obtained a polar singularity of the form 1/(s – 1), characteristic of the local limit of Green's function. The free energy density was computed as a function of the radius of the sphere r and inverse temperature using the Maple 6 pack. The results show no anomalies, indicating that there are no phase transitions to the principal order in 1/N. However, taking into account the kink–antikink configurations of the scalar field A(x) in calculations without the 1/N expansion may drastically change the phase structure of the model.     

Pseudogap in Fermionic Density of States in the BCS-BEC Crossover of Atomic Fermi Gases

We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature T _c including pairing fluctuations within a T-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature T ^* at which the pseudogap structure in DOS disappears. We also introduce another temperature T ^** at which the BCS-like double-peak structure disappears in the spectral weight. While one finds T ^*>T ^** in the BCS regime, T ^** becomes higher than T ^* in the crossover and BEC regime. We also determine the pseudogap region in the phase diagram in terms of temperature and pairing interaction.     

Electron–Phonon Interaction and Phonon Renormalization in the Lamellar Cobaltate Na x CoO2

We study theoretically the electron–phonon interaction in Na _x CoO₂. For the A _1g and E _1g phonon modes found in Raman experiments, we calculate the matrix elements of the electron–phonon interaction. Analyzing the feedback effect of the conduction electrons on the phonon frequency ω, we investigate the doping dependence of these two phonon modes. Due to the momentum dependence of the electron–phonon interaction, we find the strongest renormalization of the E _1g mode around the Brillouin zone boundary which should be observed in the neutron scattering. At the same time, the A _1g mode shows the strongest coupling to the conducting electrons around the Γ point and reveals its doping dependence in the Raman experiments. Our results shed light on the possible importance of the electron–phonon interaction in the lamellar sodium cobaltates.     

Dispersion-Induced Splitting of the Collective Mode Spectrum in Axial and Planar Phases of Superfluid 3He

The whole collective mode spectrum in axial and planar phases of superfluid ³He with dispersion corrections is calculated for the first time. In axial A-phase the degeneracy of clapping modes depends on the direction of the collective mode momentum k with respect to the vector l (mutual orbital moment of Cooper pairs), namely: the mode degeneracy remains the same as in case of zero momentum k for k‖l only. For any other directions there is a threefold splitting of these modes, which reaches maximum for k ⊥ l. In planar 2D-phase, which exists in the magnetic field (at H>H _C ) we find that for clapping modes the degeneracy depends on the direction of the collective mode momentum k with respect to the external magnetic field H, namely: the mode degeneracy remains the same as in case of zero momentum k for k‖H only. For any other directions different from this one (for example, for k ⊥ H) there is twofold splitting of these modes. The obtained results imply that new interesting features can be observed in ultrasound experiments in axial and planar phases: the change of the number of peaks in ultrasound absorption into clapping mode. One peak, observed for these modes by Ling et al. (J. Low Temp. Phys. 78:187, 1990), will split into two peaks in a planar phase and into three peaks in an axial phase under the change of ultrasound direction with respect to the external magnetic field H in a planar phase and with respect to the vector l in an axial phase. In planar phase, some Goldstone modes in the magnetic field become massive (quasi-Goldstone) and have a similar twofold splitting under the change of ultrasound direction with respect to the external magnetic field H. The obtained results as well will be useful under interpretation of the ultrasound experiments in axial and planar phases of superfluid ³He.     

Effect of Boron Substitution for Bi on Superconductivity of the Bi-2212 Phase in the Bi-Sr-Ca-Cu-O System

Possibility of boron substitution for Bi and the substitution effect on superconductivity is investigated for the Bi-2212 phase of Bi-Sr-Ca-Cu-O. From X-ray diffraction study, it is found that samples in the (Bi_2?x B _x )Sr₂CaCu₂O _z system are mainly of the single 2212 phase in a composition range of 0.0≤x≤0.6, and both of the lattice parameters a and c change with increasing x up to 0.6. From measurements of the magnetic susceptibility and the electrical resistivity, the superconducting transition temperature is found to increase up to 0.6 with increasing x. These results are considered to show that boron is substitutable for Bi up to x=0.6 in the (Bi_2?x B _x )Sr₂CaCu₂O _z system and that the boron substitution causes the number of hole-carriers to decrease in this system.     

Modifying the surface charge of single track-etched conical nanopores in polyimide

Chemical modification of nanopore surfaces is of great interest as it means that the surface composition is no longer fixed by the choice of substrate material, even to the point where large biomolecules can be attached to the pore walls. Controlling nanopore transport characteristics is one important application of surface modification which is very relevant given the significant interest in sensors based on the transport of ions and molecules through nanopores. Reported here is a method to change the surface charge polarity of single track-etched conical nanopores in polyimide, which also has the potential to attach more complex molecules to the carboxyl groups on the nanopore walls. These carboxyl groups were converted into terminal amino groups, first by activation with N-(3-dimethylaminopropyl)-N-ethylcarbodiimide (EDC) and N-hydroxysuccinimide (NHS) followed by the covalent coupling of ethylenediamine. This results in a changed surface charge polarity. Regeneration of a carboxyl-terminated surface was also possible, by reaction of the amino groups with succinic anhydride. The success of these reactions was confirmed by measurements of the pore's pH sensitive current-voltage (I-V) characteristics before and after the chemical modification, which depend on surface charge. The?permselectivity of the pores also changed accordingly with the modification.     

Hydrogenic Impurity Bound Magnetopolaron in a Two-dimensional Quantum Dot for All Coupling Strengths

The ground-state (GS) binding energies of a magnetopolaron bound to a Coulomb impurity in a two-dimensional parabolic quantum dot (QD) are studied within a variational calculation for all coupling strengths. The Lee-Low-Pines-Huybrecht variational technique that is developed previously for all coupling strength has been extended for polarons in a magnetic field. The dependence of the GS binding energies on the magnetic field, the confinement length, and the Coulomb binding parameter is investigated.     

The predominant role of collagen in the nucleation, growth, structure and orientation of bone apatite

The involvement of collagen in bone biomineralization is commonly admitted, yet its role remains unclear. Here we show that type I collagen in?vitro can initiate and orientate the growth of carbonated apatite mineral in the absence of any other vertebrate extracellular matrix molecules of calcifying tissues. We also show that the collagen matrix influences the structural characteristics on the atomic scale, and controls the size and the three-dimensional distribution of apatite at larger length scales. These results call into question recent consensus in the literature on the need for Ca-rich non-collagenous proteins for collagen mineralization to occur in vivo. Our model is based on a collagen/apatite self-assembly process that combines the ability to mimic the in vivo extracellular fluid with three major features inherent to living bone tissue, that is, high fibrillar density, monodispersed fibrils and long-range hierarchical organization.     

A Link between Spin Fluctuation and Fermi Surface in the High T c Cuprates — A Description within the Single-band Hubbard Model

A link between the spin structure and the shape of the Fermi surface is sys-tematically explored for the single-band repulsive Hubbard model with the fluctuation exchange (FLEX) approximation. We show that (i) the ex-perimentally observed band filling dependence of the peak position of the spin structure in the high T _C cuprates can be understood for both the hole-doped (YBCO, Bi2212) and electron-doped (NCCO) regimes. (ii) For La _2?xSr_xCuO₄, the spin-structure incommensurability and the ARPES re-sult for the Fermi surface can be understood simultaneously if the second nearest neighbor hopping decreases with the hole doping.     

Kim Model of Transport ac Loss with Position Dependent Critical Current Density in a Superconducting Cylinder

In this article, the dependence of the transport ac loss on field and position is investigated for a hard superconducting cylinder, which is consisted of two concentric shells with different critical current density. The Kim model is considered for the critical state in which the critical current density is assumed to depend on the flux density. Based on Norris’ equations, the analytic expression of the loss with field and position dependence is derived for the cylindrical specimen having a composite geometry. The results obtained show that the field and position dependent critical current density have obvious effects on the loss, which may explain why Norris’ predictions and the theoretical results have small differences.     

Preparation of the Silver-Superconductor Composite by Deposition of the Silver Nanoparticles in the Bismuth Cuprate Superconductor

BiSCCO (Bi–Sr–Ca–Cu–O) is high temperature superconductor with a lot of possible applications. Interfaces between superconductors and metal conductors are one of the technological problems. In this work, silver-superconductor composite was prepared by using flow of silver nanoparticles suspension in DMF (N,N-dimethylformamide) through superconductor’s pore system. Silver nanoparticles were prepared by reaction of silver nitrate with DMF. Properties of prepared composite were measured by SEM charting, XRD and critical current measurements. SEM chart showed uniform distribution of silver across sample. XRD and critical current measurements validated superconducting properties of prepared composite. In the future, materials based on this method could be used as an interface between superconductors and metals or as a base for superconducting composite with much better mechanical properties.     

The Discontinuity in the First Derivative of the ITS-90 at the Triple Point of Water

This paper investigates the discontinuity in the derivative [dW/dT ₉₀]_TPW of the ITS-90 at the triple point of water, using data for over 40 calibrated standard platinum resistance thermometers (SPRTs). It finds that the discontinuity is in most cases somewhere between 0 and ?6 parts in 10⁵, in relative terms, but that the higher numerical values are obtained for ‘less ideal’ SPRTs (those with lower temperature coefficients of resistance), and also for sub-ranges not extending beyond the indium point. These results are investigated vis-à-vis the long-standing observation that the ITS-90 reference values W _r(Ga) and W _r(Hg) are not completely consistent with data for W(Ga) and W(Hg) for real SPRTs. It discusses what may be done in a future scale to ensure continuity in the first derivative, and it concludes with a comment about the acceptance criteria for SPRTs in the scale.     

The Attractive Hubbard Model in 2-D: Is It Capable of Describing a Pseudogap and Preformed Pairs?

Deviations from Fermi liquid behavior are well documented in the normal state ofthe cuprate superconductors, and some of these differences seem to be related topretransitional features appearing at temperatures above T _c. The observationof a pseudogap, e.g., in ARPES experiments, is a familiar example of this physics. Onepotential explanation for this behavior involves preformed pairs with finite lifetimesexisting in the normal state above T _c. In this way, two characteristictemperatures can be established. A higher one T* at which pairs begin toform and the actual T _c at which a phase-coherent superconducting phaseis established. In order to test these ideas we have investigated the negative UHubbard model in two dimensions in the fully self-consistent ladder approximation atlow electron densities. In the non-self-consistent version of this theory the systemalways shows an instability toward Bose-condensation of infinite lifetime pairs. In contrastto this, pairs obtain a finite lifetime due to pair–pair interaction and thesharp two-particle bound state is strongly lifetime broadened when self-consistency isapplied. A quasiparticle scattering rate which varies linearly with temperature is alsofound. The fully self-consistent calculation we were able to perform employed ak -averaged approximation in which the self-energyloses its k -dispersion due to ak -average. This approximation is found to preservethe essential physics.