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.     

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.     

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.     

Infrared absorption ofβ-SiC particles prepared by chemical vapour deposition

Infrared absorption characteristics of-SiC particles prepared by chemical vapour deposition were studied. These particles were either solid or had a silicon core and/or were hollow. The solid particles exhibited a single absorption peak between the transverse optical frequency (_TO = 794 cm^–1) and the longitudinal optical frequency (_LO = 976 cm^–1) of-SiC. This absorption peak shifted to a lower frequency with increasing lattice parameter of-SiC and increasing free silicon content. The particles containing a silicon core and/or were hollow exhibited double absorption peaks close to _TO and _LO. The peak at the LO side shifted to a lower frequency and that at the TO side to a higher frequency with decreasing silicon core size and increasing hollow size. Using the calculations based on the effective medium theory assuming surface phonon mode, the relationship between the infrared absorption characteristics and microstructures of the-SiC particles are explained.     

Dielectric properties of thin solid films formed on silicon

We report on the measurement of the frequency-dependent complex permittivity, ()=()-i(), over the frequency range, 30 MHz to 6 GHz, of silicon wafers and of thin dielectric films formed on silicon. Measurements, as a function of temperature and time treatments, were obtained by means of an HP Network Analyzer and dielectric probe and the resulting ()and()plots for the silicon wafers are shown to have a Debye-type [1] profile, thereby indicating that the associated polarization mechanism is of the orientational variety.     

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.     

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 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.     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

The dielectric behaviour of single-crystal MgO,Fe/MgO and Cr/MgO

The dielectric constants and loss factors,, for pure single-crystal MgO and for Fe-and Cr-doped crystals have been measured at frequencies, , from 500 Hz to 500 kHz at room temperature. For pure MgO at 1 kHz the values of and the loss tangent, tan , (9.62 and 2.16×10^–3, respectively) agree well with the data of Von Hippel; the conductivity, , varies as ⁿ withn=0.98±0.02. In Fe-doped crystals increases with Fe-concentration (at any given frequency); for a crystal doped with 12800 ppm Fe, was about four times the value for pure MgO. At all concentrations the variation of log with log was linear andn=0.98±0.02. A decrease in with increasing Fe-concentration was also observed. A similar, although less pronounced, behaviour was found in Cr-doped crystals. The effects are discussed in terms of hopping mechanisms.     

Pseudogap and Superconducting Gap in YBa2Cu3o6+x: A Raman Study

We present results of electronic Raman-scattering experiments in differently doped YBa ₂ Cu ₃ O _6+x . In B _2g symmetry, an analysis of the data in terms of a memory function approach is presented and dynamical relaxation rates (, T) and mass-enhancement factors 1 + (, T) for the carriers are obtained. Starting from temperatures T > 180K, (, T) and 1 + (,T) are extrapolated to lower temperatures and used to re-calculate Raman spectra. By comparison with our data, we find a loss of spectral weight between T _c < T < T* at all doping levels x. T* is comparable to the pseudogap temperature found in other experiments. Below T _c , the superconducting gap is observed. It depends on x and scales with T _c whereas the energy scale of the pseudogap remains the same.     

Signal and noise theory for a dc SQUID amplifier

A theory is presented for the gain and noise in an amplifier based on a dc SQUID. In the lumped circuit approximation, the total inductance of the input circuitL _T is coupled to the SQUID inductanceL via a mutual inductanceM _ii = _e (LL _T )^1/2 and is in series with a voltage source with a resistanceR _i and a capacitanceC _i . The results are expressed in terms of parameters for a SQUID with reduced inductance (1– _e ² )L. The voltage gain of the amplifier at frequency /2 isM _i V ^r /Z _T ^* (), while the total voltage noise at the output of the SQUID isV _N ^r ()+M _i ² V ^r J _N ^r () (R _i + 1/jC _i )/L _TZ _T ^* (). Here,Z _T ^* ()=Z _T ()–J ^r M _i ² (R _i + 1/jC _i )/L _i , whereZ _T () is the total impedance of the unloaded input circuit,V ^r andJ ^r are the flux-to-voltage and flux-to-circulating current transfer functions of the reduced SQUID, andV _N ^r () andJ _N ^r () are the noise voltage and noise current of the reduced SQUID.     

On the maximum reduced upper critical magnetic field in Eliashberg theory

Consideration of the functional derivative of the zero-temperature reduced upper critical magnetic fieldh _c2(0) with electron-phonon spectral density ² F() suggests that its value can be maximized, for a given areaA under ² F(), with the choice of a delta-function spectral density. We show thath _c2(0) is then independent ofA and that it increases steadily as the Einstein frequency _E of the delta function is lowered. We argue that there is a local maximum inh _c2(0) at _E=0. The value at maximum is very sensitive to impurity content and increases sharply from a clean-limit value of 1.5 atT _c /_E=1.33 to more than 3.45 in the dirty limit.     

The Reissner-Sagoci problem for a non-homogeneous half-space with a penny-shaped crack

The present paper examines the elastostatic problem related to the axisymmetric rotation of a rigid circular disc bonded to a non-homogeneous half-space containing a penny-shaped crack. The shear modulus of the half-space is assumed to vary with depth according to the relation (z) = ₁(z + c), c > 0 and ₁, are constants. Using Hankel transforms, the solution of the problem is reduced to integral equations and finally to simultaneous Fredholm integral equations of the second kind. By solving numerically the simultaneous Fredholm integral equations, results are obtained which are used to estimate the stress intensity factor at the crack tip and the torque required to rotate the disc through an angle ₀.     

Linear response of a viscous liquid sheet to oscillatory external pressure perturbation in the long wave approximation. Varicose excitation

Summary. In this paper, a plane viscous liquid sheet is considered in contact with two passive media, from which two external perturbations of small intensity, given by local pressure distributions, act on the sheet. Of the two possible ways of action of the sources of perturbation only the symmetric one is pursued here, for which the sheet reacts in the so called varicose mode. The action of the sources is taken either as instantaneous, or as persisting infinitely long. During the persistent action the sources are considered to move with constant velocity along the sheet and the perturbation is changing harmonically with circular frequency _e. In the paper, the linear response of the viscous sheet to the external perturbation is computed and analyzed. The starting point of the computation is a general formula for the exact linear response of the sheet as an inverse Fourier-Laplace transform, the derivation of which is reproduced in Appendix A of this paper. The formula shows the response to depend on several characteristic numbers, of which one is intrinsic to the unperturbed sheet, whereas the others also imply the properties of the source. The intrinsic number can be taken as in which the sheet thickness h, the density of the liquid, its kinematic viscosity , and it surface tension with respect to the two ambient media enter. It is related by to the Ohnesorge number Oh. First the concept of the long wave approximation used is discussed in the context: it implies the neglect of all the hard branches _n(k),n=1,..., of spectral modes of the sheet, for which On the remaining two soft branches _±(k) of the spectrum, for which lim_k0_±(k)=0, the asymptotic expansion of (k) fork0 is considered and the whole branches are approximated by the (extrapolation of the) lowest order of the expansion. Finally, the whole Fourier integrand of the signal is substituted by its lowest order asymptotic expression aroundk=0. Within this approximation the response of the sheet to an instantaneous point perturbation is computed in its rest frame of reference. It is a long time asymptotic form of the exact response to the instantaneous point perturbation, the kernel of the general signal evolution of the sheet. The computed asymptotic form of this kernel bears a strong formal resemblance to the evolution kernel of the heat equation. The analogy is, however, not physical: whereas for ²<4 the long wave modes of the two soft branches of the sheet spectrum are purely absorptive, like the modes of the heat equation, for ²>4 their modes are dispersive and dissipative waves, with their peculiar propagation properties. By adequate application of the superposition principle the responses to instantaneous line perturbation and to harmonically persistent perturbations by moving point and line sources are computed from the asymptotic evolution kernel. Because of the specific form of this kernel, the long time surface deflection responses to the harmonic excitations do not depend separately on the additional characteristic numbers _eandW=||/ (where _eand || are considered in units of 4/h² and 2/h, respectively), but only on their ratio _e/W². The properties of these signals in dependence on and _e/W², as well as their implications for technical processes involving liquid sheets, like courtain coating, are discussed in detail.AcknowledgementThe support of this work by the German Research Foundation (DFG) is gratefully acknowledged.     

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB₂ (T _c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 < 100000 cm^–1. The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/() and the mass renormalization ratio m*()/m = 1 + () exhibit clear frequency dependence. The electron–phonon coupling strength is estimated to be 1.5 ± 0.5 while the plasma frequency _p is 2.4 eV.     

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.     

Electronic and two-magnon light scattering in oxide superconducting crystals

From investigations of two-magnon Raman scattering (RS) under high pressures up to 430 kbar in Eu₂CuO₄ and YBa₂Cu₃O_6.2 crystals, it was shown that the dependence of the superexchange integralJ on the distance between Cu and O atoms in CuO₂ planesa is anomalously weak (Ja^–n, n=3±0.5). The large value ofJ indicates strong initial overlapping of Cu and O wave functions in high-T _c , materials. It was found that an increase in free carrier concentration results in a rapid increase of magnon damping and the disappearance of the two-magnon peak from RS spectra. A detailed study of electron Raman scattering has been carried out in superconducting and insulating YBa₂Cu₃O_6–x , single crystals. The spectral redistribution at frequencies<600 cm^–1 in different polarizations indicate that the superconducting gap is strongly anisotropic. In the normal (metallic) phase the behavior of the imaginary part of the response functionR() in the polarization (xx) corresponds to the model of a marginal Fermi liquid, and in the polarization (xx), this behavior is independent of the temperature. In insulating crystals,R() is independent of temperature toT200 K in both polarizations.     

Some electrical characteristics of lithium and yttrium sialons

Some electrical properties of hot-pressed lithium sialons, Li _x/8Si_6–3x/4Al_5x/8O _x N_8–x havingx<5 and an yttrium sialon were measured between 291 and 775 K; the former consisted essentially of a single crystalline phase whereas the latter contained 98% glassy phase. For lithium sialons, the charging and discharging current followed al(t) t ^–nlaw withn=0.8 at room temperature. The d.c. conductivities were about 10^–13 ohm^–1 cm^–1 at 291 K and rose to 5×10^–7 ohm^–1 cm^–1 at 775 K. At high temperatures electrode polarization effects were observed in d.c. measurements. The variation of the conductivity over the frequency range 200 Hz to 9.3 GHz followed the () ⁿ law. The data also fitted the Universal dielectric law,() ^n–1 well, and approximately fitted the Kramers-Kronig relation()/()– =cot (n/2) withn decreasing from 0.95 at 291 K to 0.4 at 775 K. The temperature variations of conductivities did not fit linearly in Arrhenius plots. Very similar behaviour was observed for yttrium sialon except that no electrode polarization was observed. The results have been compared with those obtained previously for pure sialon; the most striking feature revealed being that _d.c. for lithium sialon can be at least 10³ times higher than that of pure sialon. Interpretation of the data in terms of hopping conduction suggests that very similar processes are involved in all three classes of sialon.