John R. Clem

Granular and superconducting-glass properties of the high-temperature superconductors

Abstract The microstructure of bulk samples of the copper-oxide high-temperature superconductors commonly is describable in terms of anisotropic grains of stoichiometric material separated by layers of nonstoichiometric interface material. The granularity strongly influences the electromagnetic properties, especially the transport critical-current density and the magnetization. In this paper, a simple theoretical model for the granularity is introduced and then used to discuss a number of electrodynamic properties (hysteretic magnetization versus magnetic field, zero-field-cooled and field-cooled magnetization versus temperature, ac susceptibility, and flux creep with logarithmic time dependence). Special attention is drawn to the importance of distinguishing between intragranular and intergranular effects.

Theory of ac losses in type‐II superconductors with a field‐dependent surface barrier

The irreversible magnetic behavior of a type‐II superconductor in a periodically varying longitudinal applied magnetic field is theoretically examined. Bulk pinning is characterized by a critical current density Jc, and surface‐barrier effects are characterized by critical entry and exit fields Hen and Hex. Theoretical expressions for magnetic field and flux‐density profiles, voltage waveforms, hysteretic‐bulk and surface‐energy losses, and the ac permeability are derived for the arbitrary flux‐density (B) dependence of Jc, Hen, Hex, and the equilibrium magnetic field Heq. Numerical model calculations are performed to demonstrate the influence of the B dependence of the latter functions upon the measurable quantities.The irreversible magnetic behavior of a type‐II superconductor in a periodically varying longitudinal applied magnetic field is theoretically examined. Bulk pinning is characterized by a critical current density Jc, and surface‐barrier effects are characterized by critical entry and exit fields Hen and Hex. Theoretical expressions for magnetic field and flux‐density profiles, voltage waveforms, hysteretic‐bulk and surface‐energy losses, and the ac permeability are derived for the arbitrary flux‐density (B) dependence of Jc, Hen, Hex, and the equilibrium magnetic field Heq. Numerical model calculations are performed to demonstrate the influence of the B dependence of the latter functions upon the measurable quantities.

Simple model for the vortex core in a type II superconductor

In order to model the core of an isolated vortex in a type II superconductor, a variational trial function for the magnitude of the normalized order parameter of the form f = ϱ/R is assumed, where ϱ is the radial coordinate, R = (p2 + ξv2)1/2, and ξv is a variational core radius parameter. Remarkably simple analytic expressions for the magnetic flux density and supercurrent density that solve Amperes law and the second Ginzburg-Landau equation are obtained. An analytic result for the free energy of the isolated vortex is then derived by integrating the Ginzburg-Landau free energy functional. The value of ξv that minimizes the free energy is calculated as a function of the Ginzburg-Landau parameter κ = λ/ξ and is found to range from ξv = 0.935ξ for κ = 0.707 to ξv ≈ 1.414ξ for κ > 1. A simple expression for the form factor or the Fourier transform of the flux density is obtained, which may be useful in the analysis of neutron diffraction experiments.

Geometry-dependent critical currents in superconducting nanocircuits

In this paper, we calculate the critical currents in thin superconducting strips with sharp right-angle turns, 180? turnarounds, and more complicated geometries, where all the line widths are much smaller than the Pearl length ?=2?2/d. We define the critical current as the current that reduces the Gibbs-free-energy barrier to zero. We show that current crowding, which occurs whenever the current rounds a sharp turn, tends to reduce the critical current, but we also show that when the radius of curvature is less than the coherence length, this effect is partially compensated by a radius-of-curvature effect. We propose several patterns with rounded corners to avoid critical-current reduction due to current crowding. These results are relevant to superconducting nanowire single-photon detectors, where they suggest a means of improving the bias conditions and reducing dark counts. These results also have relevance to normal-metal nanocircuits, as these patterns can reduce the electrical resistance, electromigration, and hot spots caused by nonuniform heating.

Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor

We have calculated the Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor for a long cylinder with elliptical cross section which approximates a long, flat strip. Our model is simplified to the two-dimensional case by assuming magnetic flux to enter in the form of a long, narrow, normal domain parallel to the axis of the cylinder. The following four contributions to the Gibbs free energy have been taken into account: (1) loss of condensation energy and gain of magnetic field energy inside the superconductor, (2) magnetic field energy outside the superconductor, (3) energy of interaction of the domain with an applied magnetic field, and (4) energy of interaction with an applied electrical transport current. Because of the Gibbs free-energy barrier, the critical magnetic field for entry of magnetic flux can be enhanced considerably above that calculated using Silsbees rule. This enhancement is found to be proportional to the square root of the width of the superconducting cylinder. Important consequences of this are the enhancement of the critical current in a superconducting strip in zero magnetic field at which electrical resistance starts to appear and a corresponding modification of Silsbees rule. We have demonstrated these effects experimentally through measurements of the onset of the current-induced resistive state in a series of superconducting indium strips of different widths and thicknesses. The experimental results confirm the theoretical predictions. The Gibbs free-energy-barrier effect described here can be interpreted as a novel flux-pinning mechanism, which might be called edge pinning.

Theory of the Magnetization of Granular Superconductors: Application to High-Tc Superconductors

We calculate the dc magnetization of a three-dimensional array of weakly Josephson-coupled superconducting grains whose dimensions are of the order of the intragranular weak-field penetration depth. Because of significant flux penetration into small grains, the initial slope of the magnetization versus applied field not only is smaller than that for very large grains of the same shape, but also decreases with increasing temperature and vanishes at the critical temperature. The same behavior is expected for the ac susceptibility versus increasing temperature in a sample cooled in zero field. The dc magnetization is found to exhibit a corresponding size-dependent suppression for all fields up to the upper critical field.

Application of low‐temperature scanning electron microscopy to superconductors

Scanning electron microscopy applied to specimens in close thermal contact with a liquid‐helium bath can be used for a two‐dimensional display of various sample responses arising from the localized excitation of the sample by the electron beam. As shown in recent experiments, the method becomes particularly interesting when applied to superconductors. A general response theory is outlined, and a detailed treatment is given for the special case of the thermal response associated with a strongly temperature‐dependent electrical resistance of the sample.

Longitudinal Proximity Effects in Superconducting Transition-Edge Sensors

We have found experimentally that the critical current of a square thin-film superconducting transition-edge sensor (TES) depends exponentially upon the side length L and the square root of the temperature T, a behavior that has a natural theoretical explanation in terms of longitudinal proximity effects if the TES is regarded as a weak link between superconducting leads. As a consequence, the effective transition temperature T{c} of the TES is current dependent and at fixed current scales as 1/L{2}. We have also found that the critical current can show clear Fraunhofer-like oscillations in an applied magnetic field, similar to those found in Josephson junctions. We have observed the longitudinal proximity effect in these devices over extraordinarily long lengths up to 290 microm, 1450 times the mean-free path.

AC losses in a finite Z stack using an anisotropic homogeneous-medium approximation

A finite stack of thin superconducting tapes, all carrying a fixed current I, can be approximated by an anisotropic superconducting bar with critical current density Jc = Ic/2aD, where Ic is the critical current of each tape, 2a is the tape width, and D is the tape-to-tape periodicity. The current density J must obey the constraint , where the tapes lie parallel to the x axis and are stacked along the z axis. We suppose that Jc is independent of field (Bean approximation) and look for a solution to the critical state for arbitrary height 2b of the stack. For c<|x|<a we have J = Jc, and for |x|<c the critical state requires that Bz = 0. We show that this implies in the central region. Setting c as a constant (independent of z) results in field profiles remarkably close to the desired one (Bz = 0 for |x|<c) as long as the aspect ratio b/a is not too small. We evaluate various criteria for choosing c, and we show that the calculated hysteretic losses depend only weakly on how c is chosen. We argue that for small D/a the anisotropic homogeneous-medium approximation gives a reasonably accurate estimate of the ac losses in a finite Z stack. The results for a Z stack can be used to calculate the transport losses in a pancake coil wound with superconducting tape.

Measurement of the ac power loss of (Bi,Pb)2Sr2Ca2Cu3Ox composite tapes using the transport technique

The transport self‐field ac loss voltages of (Bi,Pb)2Sr2Ca2Cu3Ox (Bi‐2223) multifilamentary tapes depend strongly on the voltage lead configuration. We have measured the loss voltage as a function of the measuring circuit loop size defined by the voltage leads and the tapes for well‐defined lead geometries. The loss signal was found to reach a limiting value when the length of the loop transverse to the tape was several times the tape width. This limiting voltage represents the ‘‘true’’ self‐field ac loss as predicted by new theoretical analysis.