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We describe and explain two competing regimes of ac magnetic response in current-carrying type-II superconducting wires which were observed experimentally. In the usual regime, voltage $V(t)$, induced by vortex motion across the wire, is ``in phase'' with the external magnetic field $H(t)\ensuremath{\propto}sin(\ensuremath{\omega}t)$. However, as frequency $\ensuremath{\omega}$ grows up or transport current $I$ decreases, an anomalous, ``out-of-phase'' peak in $V(t)$ appears. If these two regimes coexist, then two peaks in voltage are observed per half period of $H(t)$ in both experiment and numerical simulations. At certain combinations of $\ensuremath{\omega}, I$ and the amplitude of the external field, the out-of-phase mechanism even overwhelms the usual, in-phase one. It is shown that the out-of-phase maximum in $V(t)$ is due to the inhibition effect of zero-field (annihilation) lines on flux motion. Such lines, if present in the sample, significantly decelerate magnetic relaxation and dramatically affect the induced voltage. A phase diagram enabling one to distinguish between the in-phase and out-of-phase regimes is constructed.

We show that in superconductors of type II, where Abrikosov vortices with different polarities are present, the areas where they meet and annihilate each other ($B=0$ lines) ``attract'' a significant part of the magnetization current $j$. This leads to redistribution of $j$ over the sample, and as a result, the rate of magnetic relaxation is reduced. This effect is significant in the case of weak dependence of the activation energy $U$ on $j$, particularly for the flux flow ($U=0$) and at early stages of flux creep ($U\ensuremath{\gtrsim}kT$). The slowdown of the relaxation is mostly pronounced in the remanent state, where the $B=0$ lines are located at the edges of the sample. In the case of flux flow, the remanent magnetization decays as $m\ensuremath{\propto}1/t$ instead of the usual ``field-on'' exponential dependence $m\ensuremath{\propto}exp(\ensuremath{-}t/\ensuremath{\tau})$. The effect is important and observable in the magnetization measurements, for instance, in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ crystals and other novel superconducting materials.

Generic three-dimensional (3D) exact relations were found recently (Phys. Rev. B (2002) 184416) between macroscopic or bulk effective moduli of composite systems with related microstructures which are, in general, different. As an example of possible application of these relations, a new numerical approach is proposed for simulations of composite systems with oblate inclusions: The initially anisotropic shape of the inclusions can be transformed to spherical, but the local conductivity tensor σ 2 of the host in the initial system should be replaced by the corresponding transformed value μ 2 . We simulate large 3D networks of circuit elements in this new μ-system using relaxation, network-reduction, and other methods. The effective value of the conductivity, σ e , of the initial σ-system, can be found from the effective value μ e of the transformed μ-system, using our exact relations. We propose to apply this approach for simulations of the phase transition in the high-Tc superconducting granular ceramics.

We show, both experimentally and theoretically, that the inhomogeneous distribution of transport current produced by two contacts located at the opposite corners of a square film is significantly changed as the film becomes superconducting (the total current I flowing through the sample is kept constant). We analyze two possible sources for such a redistribution of transport current: (1) the nonlinear dependence of the resistivity $\ensuremath{\rho}$ on the current density j, and (2) the effect of surface barriers. In our geometry these sources have the opposite effect and compete with each other. This technique can be easily modified for various sample and contact geometries and is useful for the analysis of pinning and creep of vortices in superconductors.

Time dependent measurements of the electric field in BSCCO tapes carrying DC current and exposed to AC magnetic fields reveal new and rich details about the electric field behavior. In particular, E(t) curves obtained for currents above the engineering critical current exhibit "double peak" feature for each half-cycle of the external magnetic field. For currents lower than Ic, E(t) exhibits a usual sine ("single peak") with amplitude and frequency dependent phase shift relative to the external field. Similar behavior is obtained for currents above Ic for low frequencies and/or high amplitudes of the magnetic field. However, with the decrease of amplitude and/or increase of frequency, a "second peak" emerges and gradually becomes dominant. This "second peak" is in phase with the external magnetic field. We interpret the results by assuming a crossover between two regimes of flux dynamics affecting the mechanism for energy loss generation in the tape. In the "quasi-DC", low frequency - high-field regime, flux lines enter the tape from one side, cross it entirely and leave from the other side, causing a dissipation, which is in phase with the external field. In the high frequency - low-field regime, flux lines enter and leave the tape from the same side and some annihilation of vortex and anti-vortex occurs at the central region of the tape. In this regime the dissipation and its phase are frequency and amplitude dependent.

The results of a (weak) DC magnetic field induced excess resistivity in granular high-temperature superconductors are analyzed. Assuming a random mixture of superconducting and normal regions, the two characteristic excess resistivity peaks are interpreted as originating from two different mechanisms: the higher temperature peak in excess resistivity is attributed to a distribution of the critical temperature in individual grains affected by the applied magnetic field, this results in a quasi-percolative normal current energy dissipation. The lower temperature wide peak is attributed to an interplay between strong pinning due to the spatial inhomogeneity of the condensation energy on one hand and to the onset of proximity effect with decreasing temperature, on the other. The results obtained with various concentrations of Ag admixture and under varying magnetic field are consistent with the predictions of this model.

We consider a "metal" with a mean free path possessing a sharp maximum at the Fermi surface. At finite temperature, the width of this maximum is close to kBT. We show that the electrical conductivity of this system behaves as if the peak of the mean free path remains sharp at finite temperatures. In contrast to the well-known normal situation, the resistivity due to elastic scattering is surprisingly found to be linear in temperature, and the resistivity due to scattering by phonons is proportional to T2. This model is proposed to relate to some properties of "doped insulators", such as cuprates, organic metals and fullerenes.

Local magnetic measurements in a highly anisotropic Nd-Ce-Cu-O crystal reveal a sharp onset of an anomalous magnetization peak at a temperature-dependent field Bon. The same field marks a change in the field profiles across the sample, from profiles dominated by geometrical barriers below Bon to Bean-like profiles above it. The temperature dependence of Bon and the flux distribution above and below Bon imply a disorder-induced transition at Bon from a relatively ordered vortex lattice to a highly disordered, entangled vortex solid. Local magnetic relaxation measurements above Bon show evidence for plastic vortex creep associated with the motion of dislocations in the entangled vortex structure. [S0031-9007(97)04113-6]

We describe the details of a new method for studying thermally activated flux creep in superconductors. this method employs an array of microscopic Hall sensors to probe the time evolution of the field profile in the sample. We analyze these data on the basis of a continuity equation which takes into account contributions to the relaxation process from both the in-plane and out-of-plane components of the induction field. This analysis enables direct determination of flux creep parameters such as the flux-line current density, flux-line velocity and the activation energy for flux creep. We demonstrate this method by presenting experimental data for YBa2Cu3O7-x crystals in the remanent state and in the presence of a field.

We investigate surface-related transport properties of high-temperature superconductors. We find the mean vortex velocity under applied transport current determined by the activation energies for vortex penetration and exit through the Bean-Livingston barrier. We determine the current distribution between the surfaces of superconductor and the field and current dependencies of the transport activation energies. For a three-dimensional superconductor the transport activation energy, ${U}_{s}^{3\mathrm{D}}$, is found to decrease with the external field, $H$, and transport current, $J$, as ${U}_{s}^{3\mathrm{D}}\ensuremath{\propto}{H}^{\ensuremath{-}\frac{1}{2}}$ and ${U}_{s}^{3\mathrm{D}}\ensuremath{\propto}{J}^{\ensuremath{-}\frac{1}{2}}$, respectively. In the quasi-two-dimensional compounds, ${U}_{s}^{2\mathrm{D}}$ decays logarithmically with field and current. The interplay between the surface and the bulk contributions to the transport properties, such as current-voltage characteristics, is discussed.

Local magnetic relaxation measurements in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} crystals show evidence for plastic vortex creep associated with the motion of dislocations in the vortex lattice. This creep mechanism governs the vortex dynamics in a wide range of temperatures and fields below the melting line and above the field corresponding to the peak in the {open_quote}{open_quote}fishtail{close_quote}{close_quote} magnetization. In this range the activation energy {ital U}{sub pl}, which decreases with field, drops below the elastic (collective) creep activation energy, {ital U}{sub el}, which increases with field. A crossover in flux dynamics from elastic to plastic creep is shown to be the origin of the fishtail in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}}. {copyright} {ital 1996 The American Physical Society.}

We review experimental studies of the time decay of the nonequilibrium magnetization in high-temperature superconductors, a phenomenon known as magnetic relaxation. This effect has its origin in motion of flux lines out of their pinning sites due to thermal activation or quantum tunneling. The combination of relatively weak flux pinning and high temperatures leads to rich properties that are unconventional in the context of low temperature superconductivity and that have been the subject to intense studies. The results are assessed from a purely experimental perspective and discussed in the context of present phenomenological theories. [S0034-6861(96)00403-5]

Magnetic and transport phenomena in high-temperature superconductors due to magnetic flux relaxation and transport over the surface barrier are investigated. Vortex dynamics controlled by the penetration both of pancake vortices and vortex lines is discussed. The penetration field ${\mathit{H}}_{\mathit{p}}$ for pancakes decays exponentially with temperature. The size of the magnetization loop is determined by the decay of ${\mathit{H}}_{\mathit{p}}$ during the process of relaxation, but its shape remains unchanged. The irreversibility line associated with the pancake penetration is given by ${\mathit{H}}_{\mathrm{irr}}$ \ensuremath{\propto}exp(-2T/${\mathit{T}}_{0}$) and may lie both above and below the melting line.

We consider a medium-density electron gas, near the Wigner-Mott transition, immersed in a medium with a background dielectric constant e0(q, ω)that is very large at q = 0, ω = 0, but falls sharply with increasing q and/or ω. We consider the dependence of the screening parameter for state k on the energy of this state. We find that the electronic velocity is enhanced considerably at k = kF, somewhat similar to the enhancement found by Lindhard in 1954 for an unscreened electron gas. We use parameters applicable to high-Tc cuprates. We find that the maximum of v(k) around kF is very sharp, the width being a few meV, somewhat smaller than the frequency at which the dielectric constant e0(q, ω) drops. We relate this velocity peak to the normal-state transport properties of the cuprates and several other systems, and to the superconductivity. We point out specific experiments that suggest a large enhancement ofvF.

We present magnetization curves for Bi-Sr-Ca-Cu-O crystals which exhibit an anomalous second peak. Between 20 and 40 K the peak disappears gradually with time. At lower temperatures (18 K) the peak is absent in the short-time limit and it is gradually built up with time. A smooth universal function relates the magnetization at the peak (400 Oe) with that at the minimum (200 Oe) for all isotherms and at any given time, thus demonstrating the absence of the anomalous peak in the short-time limit at all isotherms.

The rate of flux creep over the surface barrier in clean HTSC samples is found. This rate proves to be significantly different for the cases of vortex entry and escape (relaxation “in” and “out”, respectively). Since a flat surface is topologically similar to the artificial columnar defects, their comparison is useful. The vortex creep over the surface is equivalent to that over the cylinder defect of radius r >λ, whereas the radii of real defects obtained so far are of order ξ λ . We discuss the effect of the smallness of defect radius on the creep process, which results in very small activation energies U at large critical current Jc. The importance of the increase of the defect radius is predicted.

The magnetic relaxation and creep of the Abrikosov vortices in high-temperature superconductors are strongly affected by surface barriers, which can dominate over the bulk pinning, especially near T c . This results in a strong difference of the relaxation rates for vortex entry and exit, non-logarithmic time dependence of the magnetic moment and other peculiarities. An competitive interplay between the surface and bulk relaxations, which gives rise to a crossover in the M (ln t ) dependence, is discussed.

Magnetic relaxation over the Bean-Livingston surface barrier is considered in high-temperature superconductors at fields Hg${\mathit{H}}_{\mathit{p}}$ (where ${\mathit{H}}_{\mathit{p}}$g${\mathit{H}}_{\mathit{c}1}$ is the first field for flux penetration) using the Clem model for a critical state with a surface barrier. The relaxation rates for vortex entry and exit are expressed through the basic thermodynamic characteristics of a superconductor. For the flux exit the magnetization M(t) depends logarithmically on time whereas for the case of entry M(lnt) appears to be a strongly nonlinear function with downward curvature, as has been found experimentally. The initial relaxation rate, dM/d lnt, proves to be much larger for flux entry than for exit, in contrast to the case of conventional bulk creep. The competing interplay between this surface relaxation and the usual bulk one, which results in a crossover in the M(lnt) curves, is discussed.

We consider a composite quasi-2D electron gas, consisting of metallic layers of width d and a background dielectric constant ϵ1, separated by layers with dielectric constant ϵ2, where d > a 0 , a 0 = h 2 ϵ 1 /me 2 and ϵ 2 ⪢ ϵ 1 . We show that the Coulomb interaction renormalizes the velocity v(k) for k ≈ kF, and v(kF) is increased by a factor close to ϵ2/ϵ1. The peak of v(k) around k = kF is very narrow. Thus the anomalous properties of an electron gas calculated by Lindhard in 1954 for an unscreened electron gas, can persist, under special conditions, even if screening is taken into account. We employ this theory to the normal-state properties of the cuprates. We find that the conductivity is increased by a factor of: [v(kF)/v(0)(kF)]2 ≈ [ϵ2/ϵ1]2 due to the velocity renormalization and the resistivity due to elastic scattering becomes temperature-dependent. We account for the conductivity anisotropy, Hall constant, thermoelectric power, and London penetration depth. Measurements of the Fermi velocity by N. Hass, employing Andreev reflection, indicate a significant increase in the velocity close to the Fermi level. This velocity renormalization increases Tc significantly.

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a 0, where a 0 = ħ2∊1/ me 2 is the Bohr radius, separated by layers with a dielectric constant ∊2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters k F a 0 and k F c ∊2/∊1. We find that when ∊2/∊1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near k F , and v ( k F ) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δ k/k F is a few percent) and becomes sharper as ∊2/∊1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T 2. Preliminary measurements suggest an increase in v k in YBCO very close to k F .

It is shown that for a quasi-two-dimensional electron gas embedded in a material with a large dielectric constant e, the plasma frequency ωp (q) for small momenta q may be less than the quasi-particle excitation energy v(kF)q. Under this condition, the screening of the Coulomb interaction is determined by the single-particle density of states. This gives rise to a significant increase of the velocity v near the Fermi surface and, in turn, to an anomalous renormalization of the transport properties. The results are applied to explain the normal properties of the high-Tc superconductors.

The resistive transition $\ensuremath{\rho}(T,H)$ in granular high-${T}_{c}$ superconductors is described by a combination of the effective-medium approximation for anisotropic mixtures with the percolation theory. We found a single parameter accounting for both the structural anisotropy as well as for the intrinsic resistivity anisotropy of a single grain. We obtained a direct (no fitting parameters) estimate of the superconducting volume fraction f as a function of temperature, as well as of the percolation threshold ${f}_{p}$ and of the zero-resisitivity threshold ${f}_{0}.$ The model describes successfully the experimental $\ensuremath{\rho}(T,H)$ dependence at different relative directions of the c axis, the current j and the magnetic field H in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8\ensuremath{-}x}$ ceramics. We provided estimates for the value of the Josephson critical current between grains. The latter proves to be strongly suppressed even by weak magnetic fields $Hl750\mathrm{Oe}.$ This results in the appearance of the field-induced excess resistivity $\ensuremath{\Delta}\ensuremath{\rho}$ that obeys the dependence $1/\ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\simeq}{1+H}_{\ensuremath{\varphi}}/H,$ where ${H}_{\ensuremath{\varphi}}$ is the characteristic field trapped by a single Josephson contact.

Measurements of magnetization curves of Y‐Ba‐Cu‐O crystals with columnar defects reveal pronounced peaks around H=0 for applied fields not parallel to the defect direction. The magnitude and direction of the remanent magnetization are independent of the direction of the applied field for a large range of angles. We show that the unidirectional character of the defects induces, in the low field limit, a flux‐flop from a direction determined by the field to the defect direction. Implications to planar pinning are discussed.

We present evidence for the importance of Bean–Livingston (BL) barriers for field penetration into high‐Tc crystals. The magnetization curves M(H) and the first field Hp for flux penetration were measured near the transition temperature Tc of untwinned Y‐Ba‐Cu‐O crystal by using a miniature Hall probe. There are three observations that serve as evidence for the efficiency of BL barriers: (1) the magnetization was found to be almost zero on the descending branch of the magnetization loop; (2) The slope of Hp(T) exhibits a clear change close to Tc, being largest at Tc; (3) after introducing damage by irradiating the sample, both the field Hp and the width of the M(H) loops reduce significantly, showing almost reversible behavior for the sample. We explain these observations in terms of BL barriers which are shown to be especially important in high‐Tc superconductors, and these could be responsible for the controversy of the Hc1 values reported previously in the literature.

Numerical studies of the flux creep in superconductors show that the distribution of the magnetic field at any stage of the creep process can be well described by the condition of spatial constancy of the activation energy $U$ independently on the particular dependence of $U$ on the field B and current $j$. This results from a self-organization of the creep process in the undercritical state $j, Comment: 12 pages, 9 PS figures

The granular HTS is treated here as a S-N mixture. Experimental data are used to determine the percolation threshold f0 (the volume fraction of superconducting grains at zero resistance) and fp (corresponding to the appearance of the first spanning superconducting cluster). The latter consists of percolating channels, each carrying the Josephson critical current Ich. We demonstrate that, knowing f0 and fp as well as the morphology and orientation of the grains, one can derive realistic estimates of Ich. This is realized by assuming a parallel resistive combination, one resistor being the spanning superconducting cluster, the other the nonspanning network. The former is treated as a percolation problem while the later is described within the effective-medium theory.

An electric field directed perpendicular to the surface of a superconductor changes the superconducting properties near the surface and creates an additional barrier for flux penetration into the sample. This effect is characterized by the value ${\mathit{l}}_{\mathit{D}}$/\ensuremath{\xi}, where ${\mathit{l}}_{\mathit{D}}$ is the Debye screening length and \ensuremath{\xi} is the coherence length, and can be neglected in conventional superconductors with ${\mathit{l}}_{\mathit{D}}$\ensuremath{\ll}\ensuremath{\xi}. However, in high-temperature superconductors, where ${\mathit{l}}_{\mathit{D}}$/\ensuremath{\xi}\ensuremath{\sim}1, the effect is very pronounced and could be used for improvement of the transport critical current.

Y-Ba-Cu-O crystals were irradiated with 5.3-GeV Pb ions. The induced columnar defects are either perpendicular or at 45 o to the Cu-O planes. Magnetization curves confirm an anisotropic, unidirectional enhancement of the critical current J c . However, a sharp crossover to isotropic enhancement is observed in the low-field limit. We interpret these results in terms of flux flop from a direction determined by the field to the direction of the defect. From this feature we determine the pinning energy of a flux line in a columnar defect

We show, both experimentally and theoretically, that the inhomogeneous distribution of transport current produced by two contacts located at the opposite corners of a square film is significantly changed as the film becomes superconducting (the total current I flowing through the sample is kept constant). We analyze two possible sources for such a redistribution of transport current: (1) the nonlinear dependence of the resistivity ρ on the current density j, and (2) the effect of surface barriers. In our geometry these sources have the opposite effect and compete with each other. This technique can be easily modified for various sample and contact geometries and is useful for the analysis of pinning and creep of vortices in superconductors.

We report an anomalous reduction of the resistivity in certain YBCO ceramics, upon applying and consequently removing a low DC magnetic field. This phenomenon is observed just below Tc, while at lower temperatures the observed remanent resistivity is higher than the pristine, similar to the characteristic “field-on” resistivity hump. We show that this effect can be interpreted as originating in an intricate interplay of the frozen-in screening currents and the superconducting percolating current in the presence of the complex intergranular boundary system.

Presentation des mesures du champ critique inferieur pour la penetration du flux, des cristaux non macles de YBa 2 Cu 3 O 7 au voisinage de leur temperature de transition T c . Ce champ decroit lineairement avec l'elevation de la temperature, mais presente une variation anormale au voisinage immediat de T c . L'irradiation electronique de basse densite reduit dramatiquement le premier champ, pour la penetration du flux. Discussion de ces resultats en termes des barrieres de surface de Bean-Livingston qui sont proposees comme etant a l'origine du retardement de l'entree du flux, et des phenomenes irreversibles dans les cristaux non irradies

Magnetic flux relaxation over the surface barrier in high temperature superconductors are investigated. Vortex dynamics controlled by the penetration both of pancake vortices and vortex lines are discussed. The penetration field Hp for pancakes decays exponentially with temperature. The size of the magnetization loop is determined by the decay of Hp during the process of relaxation, but its shape remains unchanged. The irreversibility line associated with the pancake penetration is given by Hirr ∞ exp(−2T/Tc), and may lie both above and below the melting line.

The mechanisms giving rise to the irreversibility line (IL) in the phase diagram of Bi2Sr2CaCu2O8 and the mechanism behind the second maximum in the magnetization loops were determined using a novel Hall-sensor array. The IL is caused by bulk pinning at lower temperatures and by irreversible shielding currents above 22K. The second maximum is caused by vortex lattice melting, taking place at the same local magnetic induction Bm throughout the sample.

An electric field directed perpendicular to the surface of a superconductor changes the superconducting properties near the surface and creates an additional barrier for flux penetration into the sample. This effect is characterized by the value lD/ξ, where lD is the Debye screening length and ξ is the coherence length, and can be neglected in conventional superconductors with lD⪡ξ. However, in high-temperature superconductors, where lD/ξ∼1, the effect is very pronounced and could be used for improvement of the transport critical current.

The rate of vortex relaxation over the surface barrier in HTSC is found. For the flux exit over the surface barrier the magnetization M depends logarithmically on time whereas for the case of flux entry M is a strongly non-linear function of lnt. The initial relaxation rate, dM/ dlnt , proves to be much larger for flux entry than for exit in contrast to the case of the conventional bulk creep (where these rates are approximately equal). The competitive interplay between such a surface relaxation and the usual bulk one, which results in a crossover in the M(lnt) curve, is duscussed.

The critical transport current due to surface barriers is found for high-temperature superconductors and shown to decrease as 1/ H for large magnetic fields. A self-consistent problem of the current distribution between the flux “entry” and “exit” surfaces is solved. The surface contribution is proved to be not affected by thermal fluctuations of vortex lines. Thus the surface effects on the transport properties are especially important at high-temperatures where the bulk pinning is reduced by temperature.

We present new measurements of the field distribution in untwinned single crystal of YBa2Cu3O7, using an ultra-sensitive local Hall-probe technique. In the temperature range 75 K to Tc (92.5 K), there is no field gradient along the sample when the external field is reduced. This indicates that Bean-Livingston surface barriers are the main source of magnetic irreversibility in this temperature range.