Acoustic attenuation in superfluid3He-B at low pressures

The attenuation of zero sound in superfluid³He-B has been measured up to 160 cm^–1, at pressures less than 4 bar and at frequencies 34.2, 44.2, and 54.0 MHz. The contribution of pair breaking to the attenuation has been measured for the first time. The gap (J=1 ^–) mode has been studied in magnetic fields up to 80 mT and the structure of its Zeeman components revealed. Coupling to the gap mode in the applied field allows a direct spectroscopic measurement of the energy gap. In zero magnetic field, the attenuation is well described by the theory of Wölfle, showing agreement with the magnitude of the attenuation and the frequency of the squashing mode resonance, for an appropriate choice of the parameterz=(c ₀–c₁)/c₁, wherec ₀, c₁ are the velocities of zero and first sound. This provides a determination of the Landau parameterF ₂ ^s and indicates that thef-wave interaction is negligible at these low pressures.     

Isochoric (p-π-T) measurements on liquid and gaseous air from 67 to 400 K at pressures to 35 MPa

Comprehensive isochoricp--T measurements have been carried out on liquid and gaseous air along 16 isochores at densities ranging from 2 to 32 mol · dm^–3. The air mixture has a nominal composition of 0.7813 N₂ + 0.2096 O₂ + 0.0092 Ar. Thep--T data cover a temperature range from 67 to 400 K at pressures up to 35 MPa. Comparisons with experimental results from independent sources are presented using a fundamental equation of state based. in part, on thep--T data from this study.     

Magnetic field dependence of ultrasound attenuation and sound velocity in superfluid3He-A

In the presence of a magnetic field the gap amplitude of the axial state is found to split atall temperatures if particle-hole asymmetry is taken into account. The relative gap splitting is of the order of the relative splitting of the transition temperature and leads to splittings of the frequencies of the clapping and flapping modes. The ultrasonic attenuation and sound velocity are calculated for different sound frequencies, fields, and orientations of the wave vectorq with respect to the axisl of the energy gap. The predicted splittings of the clapping and flapping mode peaks and of the cusp in the attenuation and of the step in the sound velocity at=2₀(T) should become observable at sufficiently high fields. The results are discussed in connection with ultrasonic impedance, attenuation, and velocity measurements in the A₂ and A₁ phases.     

Observation ofd-wave interference pattern:Short junction is crucial

The properties of a one-dimensional 0--Josephson junction, consiting of ans-d junction or selected boundaries between three suitably orientedd-wave superconductors, are studied. It is shown that ad-wave type interference pattern can only be observed in the field-modulated critical current if the junction is short compared to the Josephson penetration depth. However, the behavior of a 0- junction is found to be indistinguishable from that of a 0-junction betweens-wave superconductors in the long junction limit, due to the formation of a -vortex.     

Suppression of π/2−π Spin Echo in Solid 3He in High Fields

High demagnetizing field in solid ³ He leads to rich interesting phenomena such as multiple spin echoes. On the other hand, it has a severe influence on the appearance of the ordinary spin echo using /2– RF pulse sequence. We have observed spin echoes in solid ³ He in 7.4 Tesla, which appeared to decay on a much shorter time scale than T ₂ estimated from theories. This can be explained as follows. The angle made by the magnetization with the field after the -pulse differs a little from that before the pulse, because the -pulse employed in the experiment is inevitably not ideal. Since due to the demagnetizing field, the frequency of the precession motion depends on the angle between the magnetization and the field, the frequencies before and after the -pulse are different, which smeared out the spin echo. We have computed the damping time in various conditions, and found good agreement with experimental results.     

Doping-Dependent Superconducting Symmetry in Hubbard Systems

The d-wave superconducting state is studied by using a generalized Hubbard model, in which a next-nearest-neighbor correlated-hopping interaction (t ₃) is included. The results obtained within the BCS framework suggest the existence of a critical hole concentration, below which a d_x ^{2-y 2}-wave superconducting gap is observed. However, above this critical concentration the maxima of the single-particle excitation energy gap are rotated by /4 and no real nodes exist, as observed in tunneling experiments. In this study, the parameters estimated by first-principle calculations for cuprate superconductors are used.     

Energy Spectrum of Vortex Tangle

The energy spectrum of superfluid turbulence in the absence of the normal fluid is studied numerically. In order to discuss the statistical properties, we calculate the energy spectra of the 3D velocity field induced by both dilute and dense vortex tangles, whose dynamics are calculated by the full nonlocal Biot-Savart law. In the case of a dense tangle, the slope of the energy spectrum changes at k=2/l, where l is the intervortex spacing. For k>2/l, the energy spectrum has a k^–1 behavior in the same manner as the dilute vortex tangle, while otherwise the slope of the energy spectrum deviates from the k^–1 behavior. We compare the behavior for k<2/l with the Kolmogorov law.     

High Frequency Sound in Superfluid 3He-B

We present measurements of the absolute phase velocity of transverse and longitudinal sound in superfluid ³He-B at low temperature, extending from the imaginary squashing mode to near pair-breaking. Changes in the transverse phase velocity near pair-breaking have been explained in terms of an order parameter collective mode that arises from f-wave pairing interactions, the so-called J=4^? mode. Using these measurements, we establish lower bounds on the energy gap in the B-phase. Measurement of attenuation of longitudinal sound at low temperature and energies far above the pair-breaking threshold, are in agreement with the lower bounds set on pair-breaking. Finally, we discuss our estimations for the strength of the f-wave pairing interactions and the Fermi liquid parameter, F ₄ ^s .     

Microscopic Scenario for x = 1/8 Anomaly in La2 ? xSrxCuO4

We adopt a t ₁-t ₂-t ₃-J-G model for explanation of x = 1/8 anomaly in La_{2 – x} Sr _x CuO₄ family compound. The calculated charge susceptibility shows a maximum near Q = (, ) at intermediate temperatures and near (, /2) as temperature approaches zero, in agreement with neutron scattering experiments. Coulomb repulsion G between the first neighbors turns out to be the source of Charge Density Waves (CDW) in narrow band t ^eff ₁, t ^eff ₂, t ^eff ₃ < G. For physically realistic hopping values we obtain the CDW amplitude e _Q = x. The in-phase domain structure as a candidate for stripe picture is proposed.     

Zero Sound Attenuation Near the Quantum Limit in Normal Liquid 3He Close to the Superfluid Transition

The zero sound attenuation of normal liquid ³He has been studied over a range of temperatures from slightly above the superfluid transition temperature, T _c, to approximately 10mK at the constant pressures of 1 and 5bar. Using longitudinal LiNbO₃ transducers, operating both on and off resonance, the experiment was performed at 15 discrete frequencies located in several broadband frequency windows, including 16–25, 60–70, and 105–111MHz. The results are compared to Landau's prediction for the attenuation of zero sound in the quantum limit, (k _B Tk _B T _F), where ₀(P,T, )= (P) T ²{1+(/2k _B T)²}. Calibration of the received zero sound signals was performed by measuring the temperature dependence of the first sound attenuation from 30 to 800mK at those same frequencies and pressures. The data are compared to previous results.     

The influence off-wave pairing fluctuations on sound propagation in superfluid3He-A

The theory of sound propagation in pair-correlated Fermi liquids developed previously by Wölfle, with additionalf-wave pairing fluctuations, is applied to the ABM state. Expressions for the anisotropic sound absorption and velocity at arbitrary temperature and frequency in the collisionless limit are derived. Thef-wave pairing fluctuations give a large effect on the normal-flapping mode frequency at low temperatures. The corresponding shift in the sound attenuation peak of this collective mode provides a sensitive probe of thef-wave pair coupling constantg ₃. There is also a pronounced effect on the super-flapping mode attenuation peak, which becomes well defined whenf-wave pairing fluctuations are considered.     

Weak link between conventional and unconventional superconductors

In this paper we consider the Josephson coupling between a conventional and an unconventional superconductor through a constriction. It is demonstrated that a weak link is very different from a tunnel junction. In particular, in an orientation where the coupling in a tunnel junction vanishes because of symmetry, the Josephson current in the case of a weak link can nevertheless be finite, albeit with the distinctive characteristics of(i) a current phase relationship with a period of 2/n, (ii) the critical current near but below the transition temperature T ₁ of the lower transition temperature superconductor is proportional to (1–(T/T ₁)) ^n/2, where n is an integer determined by the symmetry.     

Non-linear response of internal friction to tensile strain rate and frequency during plastic deformation of high-purity aluminium

The internal friction of high-purity aluminium during the process of plastic deformation was measured by a middle torsion pendulum on a modified tensile testing machine. The effects of tensile strain rate, , in the range of 0.73×10^–6 to 50×10^–6s^–1, and frequency of internal friction measurement, f, in the range of 0.38 to 2.6 Hz were studied. The results showed a non-linear dependence of internal friction, Q ^–1, on and f ^–1 or on (=2 f). The interrelationship between internal friction during the process of plastic deformation and dislocation motion, and the effect of non-linearity on the dynamic behaviour of dislocations are discussed.     

Optical study of the Zn-substitution effect on phonon anomalies and spin gap in underdoped YBa2Cu3Oy

Performing optical reflectivity measurements with the electric field vector parallel to the c-axis of Zn-substituted, oxygen deficient YBa₂Cu₃O_y single crystals, we find a strong Zn-substitution effect on the anomaly of the inplane oxygen bending mode at 320 cm^–1 and the new absorption band at 450 cm^–1, which are observed in underdoped, non-substituted crystals. Contrary to that, the low-frequency suppression of the conductivity is almost not affected. We conclude that the phonon anomaly and the absorption band are related to each other, but that the suppression of the conductivity is an independent phenomenon. Moreover, the present work could be strong evidence for a model where some phonons couple to antiferromagnetic fluctuations at the (, )-point leading to anomalous behaviour of these phonons when a spin gap opens.on leave from Institut für Technische Physik,Forschungszentrum Karlsruhe, Postfach 3640, D-76021 Karlsruhe Germany     

Tl-NMR Study on High–Tc Oxides TlM2CaCu2O7–δ(M=Ba, Sr) : Spin-Gap in Underdoped and Overdoped Systems

The Spin–lattice relaxation rate and the Knight shift have been measured for Tl–based cuprates TlBa ₂ CaCu ₂ O ₇₊ (TB1212) and TlSr ₂ Y _l–x Ca _x Cu ₂ O ₇₊ (TS1212). In the underdoped sample of TS1212 with Tc=34K. (T ₁ ) ^–1 showed a gap–like behavior from the temperature T _SG=120K. As for the slightly overdoped sample of TB1212 with T _c =80K, both the Knight shift and (T ₁ ) ^–1 showed a significant decrease from 160K, suggesting the existing of the spin-gap not only around q(, ) but also q0.     

Analysis of the microstructure obtained by using unidirectional solidification,tungsten inert gas weld and laser surface melt traversing techniques in Al-Mn alloys

A major challenge to solidification theory over nearly three decades has been the understanding, prediction and control of rapidly solidified microstructures. The present paper reports results of systematic and controlled conditions of rapid solidification in Al-Mn alloys, which involved measurement of undercooling, solute concentration and cell spacing for solidification front velocities, which were increased progressively, to the level needed for partitionless solidification into a microsegregation-free solid which, in principle, can be crystalline, quasicrystalline or amorphous. Comparison of the measurements with predictions of theoretical modelling give an encouraging level of agreement.Nomenclature A constant = ²/P²D² - A constant = k(ab)^1/2 - B constant = mC₀p_c/D[1–pI_v(P)] - B constant - C G(Km^–1) - C _EU eutectic composition (at %, wt %) - C ₀ alloy concentration (at %, wt %) - C _L ^* tip concentration in liquid (at %, wt.%) - C _S ^* tip concentration in solid (at %, wt %) - D diffusion coefficient in liquid (m²s^–1) - G température gradient (Km^–1) - I _V(P) Ivantsov function (P exp(P)E₁(P)) - P solute Péclet number = V_SR/2D - R tip radius (m) - T _EU eutectic temperature (K) - T _F melting point of pure substance (K) - T _G arrest growth temperature (K) - T _L liquidus temperature (K) - V _ab absolute stability velocity (ms^–1) - V _s solidification front velocity (ms^–1) - a material constant - b material constant - k distribution coefficient (C_S/C_L) - k constant - m liquidus slope (K/at %, K/wt %) - n exponent - p complementary distribution coefficient (1–k) - Gibbs-Thomson coefficient (/s_f) (Km) - s _f entropy of fusion per mole (J mol^–1K^–1) - T ₀ liquidus-solidus range at C₀(T_S–T_L) (K) - ₁ cell spacing (m) - solid/liquid interface energy - 3.1416 - _c constant = 1–(2k/[1+(2/P)²]^1/2–1+2k)     

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=/2) of 20.5, 34.1, and 47.8 MHz from 30 mK to the -point T (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1–i)(f _n )^1/2 was used to measure the temperature dependence of the viscosity (T) using tabulated values of the normal fluid density _n (T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the -point,Z(T)/Z(T) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)^–2/3 nm was found, where =(T–T)/T. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as _r =8.5×10^–14 T ^–1/3 exp (8.65/T) sec. Below 1.2 K, _r >1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by f/f=2×10^–7, but the origin of this effect is not yet known.Financial support provided by the SERC, Bedford College, and the Central Research Fund, University of London.     

Ultrasonic propagation in3He-4He mixtures near the tricritical point

We present measurements of the singular sound attenuation _sing in liquid mixtures of³He and⁴He near the superfluid transition and at temperatures above the phase separation curve. The mole fractionX of³He ranged from 0.55 to 0.73 and the frequency /2 varied between 1 and 45 MHz. The temperature range was 0.75–1.4 K, with the greatest emphasis on the tricritical region nearX _t=0.67 andT _t=0.87 K. From the change in slopedU/dT of the sound velocityU, we present a new determination of the phase separation curve, which is compared with previous measurements. The sound attenuation peak along the superfluid transition becomes broader in temperature asT is decreased. In addition, there is also an increase in sound attenuation as the phase separation temperatureT is approached. ForX<X _t these two peaks merge into one asX _t is approached. For a given frequency, the attenuation has a maximum value at the tricritical point. Estimates of the contribution _D of mass diffusion to the attenuation for³He-⁴He mixtures with 0<X<0.55 and comparison with experimental values show that _D becomes relatively more important asX increases, and that atX=0.55 it effectively accounts for all of the observed singular attenuation, at least at megahertz frequencies. Hence we assume that for mixtures withX>0.55 the observed attenuation can be analyzed solely in terms of the diffusive relaxation mechanism. The mass diffusion parameterD is then determined from the data. AtX=0.55,D diverges asT is approached, which is consistent with theoretical expectations and experimental results. NearT _t, there is a crossover to a tricritical regime, and it is found that approximatelyD(T–T _t) ^Z withZ=0.32±0.1. Mode coupling predictions are thatZ=1/2 while recent renormalization group calculations giveZ=1/3. The attenuation curves in the tricritical region at the various frequencies can be represented satisfactorily but not perfectly by a scaling function with a characteristic relaxation time (T–T _t) ^–x withx=1.7±0.15. This time corresponds to order-parameter fluctuations. Its temperature dependence is in excellent agreement with renormalization-group calculations that givex5/3, while expectations from dynamic scaling are thatx=3/2. Our analysis also gives the variation of the amplitudes of andD with the direction of approach toT _t. A comprehensive theory for interpreting all the data, in the normal as well as in the superfluid phase, is lacking at this time.Supported by a grant from the National Science Foundation. A preliminary account of this work was presented inBull. Am. Phys. Soc. 21, 229 (1976).     

The Tc Amplification by “Shape Resonance” in Doped MgB2

We have applied two channels ( and ) superconductivity model to the Al_1–x Mg _x B₂. Using the experimental data, we have calculated the strength of the interchannel pairing due to quantum interference effects, probed by the interband coupling parameter, and the two gaps as a function of the x. While in MgB₂ the quantum interference effects gives an amplification of T _c by factor 1.5 in comparison with the dominant intra band single channel pairing, in AlMgB₄ the amplification is about 100, in comparison with the dominant intra band single channel pairing.     

Symmetries of Vortex Lattice Solutions of the Bogoliubov–de Gennes Equation in a Two-Dimensional Square Lattice

This report describes symmetry properties of tetragonal vortex lattice solutions of the Bogoliubov–de Gennes equation in a two-dimensional square lattice in a uniform magnetic field. The invariance group of a tetragonal vortex lattice solution is expressed in a form of G _(l) = (e + tC _2x ) (l = 0, 2, ± 1), where tC _2x is a space rotation around the x-axis accompanied with time reversal, is a kind of fourfold rotation group, and L is the magnetic translational group of the vortex lattice state. We give a new, refined definition of local symmetric order parameters (OPs) (s-wave, d-wave, and p-wave), which have a well-defined nature such that the OP (e.g., s-wave OP) at the translated site by a lattice vector (of the vortex lattice) from a site (m, n) is expressed by the OP (e.g., s-wave) at the site (m, n) times a phase factor. Winding numbers around the origin of s-wave and d-wave OPs are obtained for four types of solutions G _(l) (l = 0, 2, ± 1). It is shown that all energy bands of quasiparticles of a vortex lattice state are doubly degenerate.