Dynamic form factor of liquid4He at intermediate momentum transfer

Measurements of the inelastic neutron scattering from liquid⁴He atT=1.2 K in the range of wavevector transfer 3Q12 Å^–1 have been performed to verify the oscillations in the peak position and the width of the scattering function withQ observed by Cowley and Woods and by Martelet al. We confirm these oscillations and extend the measurements to show that the oscillations in the width continue up toQ12 Å^–1 while oscillations in the peak position, which have a much smaller amplitude, could be observed with confidence up toQ8 Å^–1 only. We also present a straightforward RPA calculation of the dynamic form factorS(Q, ), beginning from the pair interatomic potential, to see how well the observedS(Q, ) can be described and to investigate the origin of the oscillations. The observedS(Q, ) is quite well reproduced and the oscillations in the width and peak position ofS(Q, ) are seen to originate from oscillations in the interaction in the RPA which we have approximated as the⁴He-⁴He scattering amplitude calculated fromv(r). While the present calculation is quite different from the model proposed previously by Martelet al., the physical origin of the oscillations inS(Q, ) is the same, namely oscillations in the⁴He-⁴He atom scattering amplitude.     

Thermodynamic properties of the superconductorsBaPb 0.7 Bi 0.3 O 3 andBa 0.7 K 0.3 BiO 3 using Eliashberg theory

We present results of a thermodynamic analysis for the superconductors compounds BaPb_0.7Bi_0.3O₃ and Ba_0.7K_0.3BiO₃. The physical quantities are calculated making use of the Eliashberg theory and the electron-phonon spectra ²()F() as calculated by Shirai et al. For the superconductor BaPb_0.7Bi_0.3O₃, several models of the ²()F() were studied looking for a better agreement with experimental data. The best fit is achieved with a simple constant scaling (C = 1.25) of the Shirai's spectra. The functional derivative of the deviation function D(t) with respect to changes in ²()F() is also calculated.     

Excitations Beyond the Roton of Liquid 4He in Aerogel

The dynamic structure factor, S(Q, ), for wavevectors, 2.0Q3.6 Å ^–1 of liquid ⁴ He in 95% porous aerogel has been measured by inelastic neutron scattering methods. The aerogel was grown with deuterated materials and the multiple scattering involving the aerogel was negligible. S(Q, ) in the superfluid phase consists of a single peak plus broad intensity at higher energy , as in bulk superfluid ⁴ He. The single peak is identified with the phonon-roton excitation at higher Q. The weight in the peak, Z_Q , and the excitation energy dispersion curve, _Q , has the same basic wavevector dependence as in the bulk. The energy _Q is 2–3% below the bulk value at the end point and the peak is unobservable beyond Q=3 Å ^–1 within the present statistical precision. No peak is observed at T=2.3 K in normal ⁴ He suggesting, as in bulk ⁴ He, that the characteristic excitation at higher Q is associated with the superfluid phase.     

Transport results from untwinned YBCO: Washboard frequency of the vortex lattice,and the quasiparticle mean free path

The washboard frequency of the moving vortex lattice in untwinned YBa₂ Cu₃ O_6.93 may be observed through mode-locking to an externally applied ac current of frequency _ext. The interference between and _ext results in jumps in the dc current-voltage characteristics when and _ext are harmonically related¹. The interference effect disappears in the vortex liquid state. The Hall conductivity _xy below T_c in YBCO contains contributions² from a positive quasiparticle (qp) term (H) and a negative vortex term (1/H). The qp term is surprisingly large well below T_c and implies a large gap anisotropy and a long qp mean free path (mfp). The thermal Hall effect³ _xy is closely related to the qp _xy; _xy is produced by asymmetric scattering of qp by pinned vortices. The qp mfp at H = 0, extracted from _xy and extended to low T by _xy, increases remarkably from 90 Å at T_c to more than 0.5m at 22 K.     

Room temperature age-hardening in a β titanium alloy

A metastable titanium alloy containing 10 wt % Zr and 12 wt % V has been found to undergo a substantial age-hardening reaction at temperatures as low as 20° C. The reaction involves continued growth of athermal-phase particles produced during water quenching from the-phase field. The morphology of the as-quenched is retained, implying the absence of long-range diffusion during ageing: this is consistent with the low value of the activation energy measured (93 kJ kg mol^–1). It is suggested that the growth is caused by unpinning of/ interfaces as a result of the short-range motion of interstitials present in the alloy. The age-hardening produces a severe loss in tensile ductility and inhibition of stress-induced martensite formation.     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

Odd frequency pairing in superconductors

The properties of a superconductor having an energy gap function _k( _n ) which is an odd function of frequency _n, or time, are investigated. One finds (a) the allowed pair orbital angular momenta for spin zero and spin one are interchanged, permittingS= 0, l=1 and S=1, l=0 condensates; (b) there exists an equal-time order parameter corresponding to condensation of a spin wave coupled to two fermions, in contrast to the conventional timereversed fermion pair condensate; an explicit energy gap equation is derived for this composite operator condensate; (c) the coherence factors are shown to be reversed from those of conventional pairing, for>2, removing the peak in thea+C conductivity() and generating a peak in the>2 acoustic attenuation as a function of temperature; (d) the Josephson current vanishes between an even and odd frequency superconductor, and vanishes to leading order in the tunneling rates t ₁₂ ² .The authors wish to acknowledge the support of the National Science Foundation, grant No. DMR92-13295 (J.R.S.) and No. DMR 92-205027 (D.J.S.). They would like to thank Leo Lilly and William Putikka for helpful discussions.     

Superconductivity in amorphous Bi and Ga

The electron-phonon ²()F() has been measured by Chenet al. in films of amorphous Bi and Ga. This was accomplished by inversion of low-temperature quasiparticle tunneling data. From ²()F(), the phonon renormalization of the electronic effective mass was calculated and was found to be considerably greater than it is in the case of the well-known strong-coupling superconductors Pb and Hg. These amorphous materials should, therefore, be ideal for a study of strong-coupling effects, i.e., deviations from BCS laws. In this paper, we present results of a theoretical study of select thermodynamic properties of these materials based on numerical solutions, at finite temperatures, of the Eliashberg equations.Work performed under the auspices of the U.S. Atomic Energy Commission, and supported in part by the National Research Council of Canada.     

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

The zero sound attenuation, ₀(,T, P), of normal liquid ³ He has been studied over a broad range of frequency (/2 = 8 – 50 MHz). Data has been collected at a constant temperature (T 1.1 mK) which is just above the superfluid transition temperature, T _c , when the liquid is near a pressure, P, of 1 bar. The results are compared to Landau's prediction in the quantum limit, k _B T k _B T _F , where ₀(,T,P) = (P) T ²[l + (/2k _B T)²]. Deviations from Landau's prediction are compared to the results of other workers and are discussed with respect to additional (unidentified) extrinsic background effects and (possible) intrinsic scattering mechanisms due to fluctuations in the liquid.     

Transverse acoustic impedance of normal liquid3He

Both the real and imaginary parts of the transverse acoustic impedance of normal liquid³He have been measured at excitation frequencies of 10 and 30 MHz, fluid pressures from 0.7 to 27 bar, and temperatures from 3 mK to 1 K. The impedance is obtained from the changes in resonance frequency and Q of a quartz crystal, which is electrically driven to oscillate in a thickness shear mode while immersed in liquid³He. These results are compared with the predictions of Fermi liquid theory, which takes into account two contributions to the impedance: (1) incoherent single-quasiparticle excitations, and (2) the excitation of the collective transverse sound mode. At 0.7 bar, our measurements of the impedance are in agreement with the predictions of Fermi liquid theory and imply that the symmetric Fermi liquid parameterF ₂=1.25±0.4 ifF ₁=6.3. At higher pressures, we also observe agreement in the region <0.3, where is the excitation frequency and is the quasiparticle scattering time. However, above 8 bar in the zero-sound regime (1), the impedance is observed to be frequency dependent, at constant . This frequency dependence cannot be explained within the present framework of Fermi liquid theory.This work was supported by the National Science Foundation under Grants DMR 76-02043 and DMR 78-08650.     

Anomalous normal state and high temperature superconductivity in the cuprates

It is generally believed that a high electronic density-of-states n(E_F), and therefore a low Fermi velocity v_F, are required to obtain a high transition temperature, since T_{c ph} exp(–1/) and = n(E_F)V. However, V = < I² >/M _ph ² , and Bardeen showed that I E_Fk_F = (1/2)k _F ² v_F. Thus one may expect that should increase with v_F. While it may not be feasable to increase the one-electron velocity v_F signifcantly, the velocity may increase greatly as a result of renormalization by electron-electron interactions. Such a renormalization exists in Hartree-Fock theory for an unscreened electron-gas. We found that for a medium-density electron-gas (r_s 10–20) imbedded in a background with a dielectric constant () such that / > 10, there is a significant increase of v_F by renormalization, even when screening is taken into consideration. The peak of v(k) at k = k_F is very narrow, the half width being somewhat less than the frequency ₀ at which () falls by a factor of 2. When () is due to ionic polarization, _o is a typical phonon frequency. The height of the peak v_F/v _F ⁰ is of order E_F/₀, and the width in units of momentum is: k/k_F (₀/E_F)². This velocity peak is associated with a minimum in the screening constant at E_p. Its sharpness causes the normal state properties to be highly anomalous; namely the conductivity is exceptionally high, with an anomalous temperature dependence; the conductivity anisotropy, thermoelectric power, and Hall constant are anomalous. Direct determination of v(k) in YBCO by several methods indeed suggests a large, sharp peak, the width being of order 10 me V. This peak manifests itself in the tunneling and point-contact spectroscopy I–V curves. We suggest that the reduced screening at the Fermi level, associated with this velocity peak, is responsible for the high T_c of the cuprates and several other exotic superconductors. Thus, the high T_c is a reflection of the anomalous normal-state properties.     

Theory of periodically driven,current-carrying,superconducting filaments. I. Spatially homogeneous states

Starting from the nonequilibrium theory of dirty superconductors in the Ginzburg-Landau regime, spatially homogeneous states with an applied currentI=I ₀+I ₁ cos (t) are considered. Expressions for the linear response (I₁ small) valid up to high frequencies (k _BT_c) are derived and evaluated analytically for the experimentally important case of smallI ₀ and ₀(T). Then the nonlinear response is treated for frequencies with _E1. Interesting new behavior is found for frequencies ₀ 1, where ₀ is essentially the GL relaxation time.     

Absence of Phase-Fluctuation Contribution to the Low-Frequency Optical Conductivity in d-Wave Superconductors at Zero Temperature

The behavior of the low-frequency optical conductivity _reg() in superconducting cuprates is, at the present, an open and interesting issue. In particular, since the zero-temperature and zero-frequency limit of _reg() attains a value much larger than the universal value expected within a self-consistent T-matrix calculation, an intriguing possibility is that the collective mode can also contribute to _reg(). By taking into account the effect of dissipation on the collective mode in a d-wave superconductor, we evaluate the phase-fluctuation contribution to _reg(0) within the formalism of the phase-only action. We show that even though the collective mode contributes to _reg() at finite frequencies, approaching the zero-temperature and zero-frequency regime the corrections at _reg() due to phase fluctuations vanish.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

Deformation Phenomena on the Charged Helium Film in Presence of Cyclotron Pumping

The possibilities are discussed for the investigation of 2D quasienergetic electron states on liquid helium surface in presence of the normal magnetic field and a.c. electric field E with the frequency _c, where _c is the cyclotron frequency.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Theory of neutron scattering from the two-roton,two-maxon and maxon-roton states in superfluid4He

In 1970, Ruvalds and Zawadowski (RZ) outlined a microscopic theory of the two-roton pair excitation spectrum in superfluid⁴He. They pointed out that because of a Base condensate-induced coupling into the density fluctuation spectrum, these pair excitations show up in inelastic neutron data for S(Q, ) as high energy multiparticle scattering above the maxon-roton quasiparticle peak. Stimulated by recent high-resolution neutron data from ILL, we have carried out an extensive study of the single-particle ₁(Q, ) and the two-particle ₂(Q, ) spectral densities within the RZ scenario, over a wide range of wavevectors (1 Q 3 Å^–1), frequencies and temperatures. We extend the original RZ analysis (which concentrated on the two-roton spectrum) to include the multiparticle structure associated with the maxonroton and maxon-maxon spectra and present numerical results for both attractive and repulsive quasiparticle interactions. We also point out that the microscopic theory of S(Q, ) in a Bose-condensed fluid shows that it involves a weighted sum of both ₁(Q, )and ₂(Q, ). As a result, multiparticle structure exhibited by S(Q, ) is not easily related to theoretical results for ₁(Q, ) and ₂(Q, ). Previous attempts in the literature to fit neutron data for S(Q, ) to either ₁(Q, ) or ₂(Q, ) would not appear to have much quantitative basis, especially in the two-roton frequency region 2_R.     

Dielectric properties of chemically vapour-deposited Si3N4

The dielectric properties of chemically vapour-deposited (CVD) amorphous and crystalline Si₃N₄ were measured in the temperature range from room temperature to 800° C. The a.c. conductivity ( _a.c.) of the amorphous CVD-Si₃N₄ was found to be less than that of the crystalline CVD-Si₃N₄ below 500° C, but became greater than that of the crystalline CVD-Si₃N₄ over 500° C due to the contribution of d.c. conductivity ( _d.c.). The measured loss factor () and dielectric constant () of the amorphous CVD-Si₃N₄ are smaller than those of the crystalline CVD-Si₃N₄ in all of the temperature and frequency ranges examined. The relationships of ^n-1, (- ) ^n-1 and/(- ) = cot (n/2) (were observed for the amorphous and crystalline specimens, where is angular frequency andn is a constant. The values ofn of amorphous and crystalline CVD-Si₃N₄ were 0.8 to 0.9 and 0.6 to 0.8, respectively. These results may indicate that the a.c. conduction observed for both of the above specimens is caused by hopping carriers. The values of loss tangent (tan) increased with increasing temperature. The relationship of log (tan) T was observed. The value of tan for the amorphous CVD-Si₃N₄ was smaller than that of the crystalline CVD-Si₃N₄.     

Effects of phonons and antiferromagnetic spin fluctuations on the pairing and density of states in high-T c superconductors

We solve the Eliashberg equations for a two-dimensional, tight-binding band and anisotropic interaction due to exchange of phonons and antiferromagnetic spin fluctuations. For small band fillings, a mixture of simple and extendeds-wave pairing is stable, while for band fillings closer to half-filling thed-wave pairing state becomes stable. The density of statesN() becomes highly asymmetric in for smaller band fillings, which is an effect of particle-hole asymmetry. For thed-wave stateN() is linear in for small and exhibits a logarithmic singularity at the gap amplitude. For the mixeds-wave stateN() shows the BCS singularity at the gap edge. Antiferromagnetic spin fluctuations give rise to a pseudogap inN() for the normal state.     

Effect of composition on optical properties of co-evaporated Mn/SiO x,Cr/SiO x and Cu/SiO x cermet thin films

Optical absorption spectra of amorphous Mn/SiO _x , Cr/SiO _x , and Cu/SiO _x cermet films, 300 nm thick, with compositions from 0 to 25 at% Mn, Cr and Cu, respectively, prepared by co-evaporation at 293 Kin vacuo have been investigated. The linearity of ()^1/2 versus graphs in the high absorption region for all the cermet films indicates that indirect photon transitions in k-space are involved in the absorption process. Taue's rule is also confirmed. In all cases the optical energy gap decreases significantly with increasing metallic content of the films and the width of the tail of localized states increases.