Free Energy of a d-Wave Superconductor in the Nearly Antiferromagnetic Fermi Liquid Model

A very general Hamiltonian which describes the coupling of charge carriers via a spin susceptibility is used to derive a formula for the free energy difference between the superconducting and the normal state of a d-wave superconductor. The formula is then specialized to the nearly antiferromagnetic Fermi liquid (NAFL) model and evaluated numerically. The comparison with specific heat data measured for optimally doped YBa₂Cu₃O_6.95 reveals the necessity to include even contributions far away from the Fermi surface to the free energy. The usual restriction to a narrow shell around the Fermi surface in deriving the free energy formula is proved to be inadequate.     

Dielectric response functions in the problem of longitudinal collective mode excitation in superconductors

General methods of the electrodynamics of media with spatial and frequency dispersion are used to develop a formalism for the dielectric functions of the response of a superconducting metal to electromagnetic perturbations. The transformation of electromagnetic waves into long-wave oscillations of the longitudinal field in a superconductor is investigated. The temperature and frequency dependences of the collective mode contribution to the superconductor surface impedance are found. Resonant excitation of a collective mode in superconducting samples of finite size is predicted, which may result in selective transparency of superconducting films.     

Intrinsic Pinning in the Layered Superconductor YBa2Cu3O7 Studied by the Conversion of Ultrasonic to Electromagnetic Waves

Intrinsic pinning in a single-crystal YBa₂Cu₃O₇ superconductor has been investigated through the conversion of ultrasonic to electromagnetic waves. The interaction with a longitudinal ultrasonic wave was dramatically enhanced as a result of the intrinsic pinning of the vortex so as to form a sharp peak when a dc magnetic field was applied nearly parallel to the superconducting plane. Not only the height but also the angle width of the peak decreased with the temperature increase because of the weakening two-dimensionality. The crossover between the intrinsic pinning and the point-defect pinning is discussed by taking into account the pinning strength.     

Deformation attenuation of ultrasonic shear waves in aluminum

The deformation contribution to the electronic attenuation of ultrasonic shear waves in aluminum is measured to be of the same order of magnitude as for longitudinal waves. This real metal effect is found highly anisotropic, depending both on the directionq/q and the polarization ε of the ultrasound. An anisotropic deformation parameterK _y is therefore suggested as being large whenever ε is close to the edgeWK of the Fermi surface.     

Ultrasonic attenuation studies in molybdenum

The electronic attenuation of longitudinal and shear waves has been measured in both the normal and superconducting states of molybdenum. In all cases the limiting attenuation is an order of magnitude larger than the free-electron prediction. A model based on the tight-binding approximation is proposed to explain these results and the absence of a rapid-fall region in the superconducting shear wave attenuation.Work supported by National Science Foundation.     

Absorption of ultrasound in the intermediate state of indium

The attenuation of longitudinal ultrasonic waves has been measured in spectroscopically pure single crystals of indium in the intermediate state over the frequency range of 10–30 MHz. It is shown that the total attenuation in the intermediate state can be divided into two parts. The superconducting layers give rise to the oscillatory temperature-dependent attenuation, while the normal layers and the boundary effect between the normal and superconducting layers produce a temperature-independent constant attenuation. A plausible explanation of the observed experimental results is discussed.     

Resonance Tunneling of Electromagnetic Waves for Enhancing the Efficiency of Bolometric Photodetectors

A method for enhancing the efficiency of bolometric photodetectors is presented. The method utilizes the analogy between the process of tunneling of a flux of quantum particles through a potential barrier and the propagation of electromagnetic waves within a nontransparent medium. The calculation results demonstrate that the fraction of radiation absorbed in a detector at a certain IR frequency may be close to unity if one chooses the right thickness and permittivity of the resonator substrate below a thin metal (superconductor) layer.     

Surface acoustic wave determination of the superconducting fraction of a Nb3Ge film

Surface acoustic waves at 1200 MHz were used to investigate the properties of a 0.5-µm-thick film of Nb₃Ge. This film was rf-sputtered onto a substrate consisting of a piezoelectrically active 3.5-µm AlN layer which was chemically vapor-deposited over a sapphire substrate. The attenuation coefficient of the surface acoustic waves was measured from 0.8 to 30 K. The raw data are analyzed to eliminate interference effects due to splitting of the wave into two components. One of these is at the surface of the film and the other may be a surface skimming bulk mode which is at the film-substrate interface. The resultant curve of attenuation versus temperature in the superconducting region is then used to determine the distribution function of the superconducting transition temperature of the film. Although the film starts to become superconducting at 21 K and the majority of the film appears to become superconducting at 18 K, it is also found that a significant amount of the film does not become superconducting until 10 K. The difference between the attenuation measured in the normal state and the superconducting state is used to obtain the electron mean free path in the film. This is compared to values obtained from electrical measurements.Research supported by the U.S. Air Force Office of Scientific Research under Grant No. AFOSR 81-0002.Research supported by the U.S. Air Force Office of Scientific Research under Contract No. AFOSR F49620-78-C-0031.     

Thermodynamic Properties of a d-Wave Superconductor Near Zero Temperature

On the basis of Fermi liquid theory, we study the thermodynamic properties near zero temperature of a d-wave superconductor assuming the BCS pairing model. The temperature dependence of the order parameter is derived. We then obtain an analytical expression for the free energy difference between the normal and superconducting states in the vicinity of zero temperature from the coupling constant integral. New expressions for the critical field and the specific heat in the superconducting state are given as functions of temperature. We compare our expressions with previous formulas due to others.     

Thermodynamic Properties of a d-Wave Superconductor Near Zero Temperature

On the basis of Fermi liquid theory, we study the thermodynamic properties near zero temperature of a d-wave superconductor assuming the BCS pairing model. The temperature dependence of the order parameter is derived. We then obtain an analytical expression for the free energy difference between the normal and superconducting states in the vicinity of zero temperature from the coupling constant integral. New expressions for the critical field and the specific heat in the superconducting state are given as functions of temperature. We compare our expressions with previous formulas due to others.     

Transverse and longitudinal ultrasonic attenuation measurements of the superconducting energy gap in high-purity rhenium

The attenuation of transverse and longitudinal waves propagating along thec axis in high-purity rhenium has been measured in the normal and superconducting states. In the superconducting state the attenuation was compared with the simple BCS theory using as adjustable parameters the gap parameter and the residual attenuation atT _c (for transverse waves). Using transverse-wave attenuation a gap parameter of 3.50±0.10 was found, while the longitudinal attenuation data yielded a gap parameter of 2.90±0.10. At present, the only apparent explanation for this difference is that the integrals for transverse-and longitudinal wave energy loss in an ultrasonic wave contain different azimuthal angle dependencies and thus average an anisotropic energy gap differently.Research sponsored by the Air Force Office of Scientific Research under AFOSR Grant No. 71-2079.     

RETRACTED ARTICLE: Cooperative Time-Reversal Symmetry Breaking Induced by a Magnetic Field in a Quasi-2D d-Wave Superconductor

A model of quasi-two-dimensional d-wave superconductor, with strong nesting properties of the Fermi surface is considered. The orbital effect of a moderate magnetic field applied perpendicularly to the conducting planes is studied in the mean field approximation. It is shown that the field can induce a time-reversal symmetry-breaking spin density wave order coexisting with the superconducting order and can open a gap over the whole Fermi surface. The anomalies recently observed in the heat conductivity, penetration depth, and zero-bias conduction in cuprates might be ascribed to this effect.     

Cooperative Time-Reversal Symmetry Breaking Induced by a Magnetic Field in a Quasi-2D d-Wave Superconductor

A model of quasi-two-dimensional d-wave superconductor, with strong nesting properties of the Fermi surface is considered. The orbital effect of a moderate magnetic field applied perpendicularly to the conducting planes is studied in the mean field approximation. It is shown that the field can induce a time-reversal symmetry-breaking spin density wave order coexisting with the superconducting order and can open a gap over the whole Fermi surface. The anomalies recently observed in the heat conductivity, penetration depth, and zero-bias conduction in cuprates might be ascribed to this effect.     

Radiation of terahertz electromagnetic waves from build-in nano Josephson junctions of cuprate high-T(c) superconductors

The nano-scale intrinsic Josephson junctions in highly anisotropic cuprate superconductors have potential for generation of terahertz electromagnetic waves. When the thickness of a superconductor sample is much smaller than the wavelength of electromagnetic waves in vacuum, the superconductor renders itself as a cavity. Unlike conventional lasers, the presence of the cavity does not guarantee a coherent emission because of the internal degree of freedom of the superconductivity phase in long junctions. We study the excitation of terahertz wave by solitons in a stack of intrinsic Josephson junctions, especially for relatively short junctions. Coherent emission requires a rectangular configuration of solitons. However such a configuration is unstable against weak fluctuations, contrarily solitons favor a triangular lattice corresponding to an out-phase oscillation of electromagnetic waves. To utilize the cavity, we propose to use an array of stacks of short intrinsic Josephson junctions to generate powerful terahertz electromagnetic waves. The cavity synchronizes the plasma oscillation in different stacks and the emission intensity is predicted to be proportional to the number of stacks squared.     

高频电磁力作用下金属液内电磁超声波的生成

为解决由机械振动产生的超声波无法在高温环境中成功应用的难题，提出了利用静磁场和交流电流、静磁场和交流磁场的相互作用分别在金属液内直接生成高强度电磁超声波的方法，运用超声波压力传感器对用这两种方法在金属液内生成的电磁超声波的强度进行了测量。研究表明：电磁超声波的强度与所施加的高频电磁力的强度成正比，频率与电磁力的频率相同；实验结果和理论解析结果基本一致；利用高频电磁力的局部作用在金属液全场范围内生成的电磁超声波可以在金属精炼及凝固过程中获得广泛应用。     

Ultrasonic attenuation in the superconducting and intermediate states of pure and doped type I superconductors

The attenuation of longitudinal ultrasonic waves has been measured in single crystals of indium (99.999%), indium doped with 0.003 at % of tin, and indium doped with 0.002 at % of bismuth in the intermediate and superconducting states over the frequency range 10–30 MHz. For the bismuth-doped indium specimen, measurements were taken for three different physical states, i.e., for three different dislocation densities, and for the indium and the tin-doped indium specimens, measurements were for one physical state. For a particular measurement, the same physical state was maintained both in the intermediate and superconducting states. A temperature-dependent oscillatory behavior of the ultrasonic attenuation was observed in the intermediate state in all the three specimens, but in the superconducting state the oscillatory behavior was observed only in the bismuth-doped specimen. Two phases have been identified in the superconducting layers of the intermediate state and there is only one phase in the superconducting state of the bismuth-doped sample. The origin of the two phases in the intermediate state and that of the single phase in the superconducting state of the bismuth-doped sample are discussed. A qualitative explanation is presented for the occurrence of oscillatory attenuation in the intermediate state irrespective of the nature of the dopant and the selective occurrence of oscillatory attenuation in the superconducting state due to the nature of the dopant.     

Effect of metal oxides addition on the superconducting properties of YBaCuO

The superconducting properties of YBCO superconductor with ZrO2 addition prepared by different contents were prepared by a unique method so called thermal pyrolysis process to study the effect of the zirconium oxide on the electromagnetic properties and superconducting mechanism of the superconductor. The critical temperature of YBCO superconductor was not predominately dependent upon the zirconium oxide. The maximum magnetism was observed by adding 2% zirconium oxide. The addition of zirconium oxide forming a pinning center of magnetic flux due to ZrO2 phase which was related to the change of electromagnetic properties of the YBCO superconductor. The result indicates that magnetization is proportional to the number of magnetic flux lines passing through the sample. The added ZrO2 appear to contribute the increasing Vickers hardness.     

On the feasibility of high spatial resolution superconducting X-ray detectors

We discuss a class of superconducting particle/radiation detectors in which the readout is by magnetic means. Even a small energy deposition can change the state of a superconductor, leading to a drastic change of its electromagnetic properties. To increase the detector sensitivity, a highly granulated superconducting medium is used. Millions of physically separated sensors are read out in parallel by only a few channels of very sensitive D.C.-SQUID based electronics. We present the mathematical formulation of the problem and discuss how the excellent signal-to-noise ratio obtained using SQUIDs permits us to determine particle/photon localization.     

Longitudinal ultrasonic attenuation coefficient for high-T K Kondo superconductors

The ultrasonic attenuation coefficients for longitudinal waves in bulk superconductors containing high-T _K Kondo impurities and in proximity effect sandwiches containing the Kondo impurities in the normal layer are obtained using the Matsuura, Ichinose, and Nagaoka approach to treat the scattering by the Kondo impurities. The attenuation coefficients are obtained for temperatures close toT _c by suitably renormalizing the propagators and vertices appearing in the leading graphs in the expansion of the density-density correlation function appearing in the definition of the longitudinal attenuation coefficient for the case ql1. Closed-form expressions for the attenuation coefficient for the bulk superconductor case are obtained.     

Peculiarities of transport current penetration in a composite superconductor taking into account different models of flux creep

The flux-creep diffusion of transport current in superconducting composite slab and cylinder based on a hard superconductor is investigated theoretically. Power and exponential current-voltage characteristics were used to define the electric field in the flux-creep regime. Using scaling solutions, the Maxwell equations describing transport current penetration in a one-dimensional superconducting composite are solved analytically. A proposed analysis indicates the existence of special macroscopic distribution of electromagnetic field in superconductor during the flux creep. It is shown that the flux-creep electromagnetic field cannot promptly propagate into the composite and penetrates at the finite rate like in the flux-flow regime. Therefore, a moving current boundary exists in the superconducting composite. It separates the region where the current flows from free current region. Moreover, in the flux creep specific conditions are fulfilled at moving boundary in contrast to the flux-flow regime. According to these conditions the electric and magnetic field induced by current charging smoothly approach to its undisturbed values. They are independent of any parameters of current-voltage characteristics and appear due to zero value of the differential resistivity of the composite at moving boundary. To confirm these results, the numerical calculation based on more general model is executed. The equations describing the violation of stable distribution of fully penetrated current are defined.