Limiting currents in fermionic superconducting strings

It is usually assumed that the critical current in a fermionic superconducting string is of order em, where m is the in vacuo mass of the charge carrier. It is argued here that in reality the critical current is of order em²R, where R is the string's radius of curvature. This has some important consequences: in particular, scattering amongst the charge carriers can be shown to limit the current to less than roughly 10⁹ GeV.     

Persistent currents in superconducting quantum interference devices

Starting from the reduced dynamical model of a two-junction quantum interference device, it shown that a quantum analog of the system can be exhibited. This quantum model extends the well-known properties of the device when its characteristic dimensions are of the order of mesoscopic length scales. By finding eigenvalues of the corresponding Hamiltonian operator, the persistent currents flowing in the ring have been obtained. The resulting quantum analog of the overdamped two-junction quantum interference device can be seen as a supercurrent qubit operating in the limit of negligible capacitance and finite inductance.     

Persistent currents induced in the superconducting surface sheath

The magnetization curves of type 2 superconductors, and type 1 super-conductors, for which H _c3>H _c, show a hysteretic tail in a range of field below H _c3 which corresponds to a persistent current induced in the super-conducting surface layer (the sheath). Existing theories of this magnetization M are based on the hypotheses (a) that departures of the current distribution from uniformity are confined to the ends and may be neglected for long enough cylinders, and (b) that at the persistent (‘critical’) current, the free energy has the same value as it does in the normal state. These are the essential assumptions of what we call the infinite cylinder model. The apparent differences between the results of calculations based on this model made by Fink et al. and those made by Park, are shown to reside in a parameter η which Fink et al. assume to be ～1. Values of η for a number of values of field and Ginzburg-Landau parameter κ are given. In a certain range, η ～ 1 but η deviates markedly from 1 when κ is large (η∝ κ^1/2 then), and at low fields when κ is small. It is shown that according to the model the tail should be symmetrical about the M=0 axis but that in order to show that it should be so, from free energy arguments, one must take into account the magnetization m of the sheath itself (due to its internal currents) even though m makes a negligible contribution to the total magnetic moment. The theory is compared with experiment, and significant discrepancies are found, particularly in the field dependence of M near H _c3, which cannot be explained away as being the result of imperfections in specimen quality.

The problem is then reconsidered on the basis of less arbitrary assumptions. First we consider the thermodynamic stability of the sheath. It is necessary to discuss the problem in terms of the current (per unit length, always) rather than magnetization M, so that we may distinguish between current in some particular region of the cylinder from the current averaged over its whole length. The average current J is directly related to the average magnetization M. Adopting the sign convention that a positive current produces a diamagnetic moment, M = ?J. The continuous sheath will become unstable when the free energy in the presence of a break in the continuity over a small patch of surface is reduced by an increase in the area of the patch. That is our basic assumption. Unlike the homogeneous systems normally considered in thermodynamics, the sheath becomes unstable at an average current J which depends on the shape and position of the patch. If the patch lies in the central region of the cylinder the associated critical current J ₁>>j _c, where j _c is the critical current calculated according to the infinite cylinder model. If it forms a ring of constant width on one end the sheath becomes unstable at J ₂=j _c. Thus the free energy criterion used to calculate j _c corresponds to the assumption that J ₂ is the lowest current at which the sheath becomes unstable. It is shown that the sheath may become unstable to penetration from the end along a large number of narrow slots at a current J ₃?-j _c. Whether or not J ₃<j _c, however, the sheath would always begin to break up at the end if the current reached a value J _u before it became unstable. J _u is the average current at which the current on the rim of the continuous sheath would reach j _u. j _u is the ‘ultimate’ current, the maximum current the sheath can carry under any circumstances. We show that for a high κ superconductor J _u<j _c, and assume the same inequality to hold for low κ superconductors. Thus at a certain current J _p the sheath begins to break up at the end, and at this point, we argue, vortices or ‘flux spots’, of the type whose existence has been proposed by Hart and Swartz, enter the sheath from the ends. J _p equals either J _u or J ₃, whichever is smaller. Only if J _p equals J ₃ does it correspond to a thermodynamic instability. In any case, since J _u<j _c, J _p<j _c, so that j _c does not correspond to any observable phenomena, though it is a function with some heuristic value. Unless there is no pinning of the flux spots at all it will not be until a higher (average) current J_k that the spots move continuously through the sheath, entering it at one end and leaving it by annihilation with spots of opposite sign in the middle. It is this current J_k to which the magnetization tail corresponds. Above J _p there are observable effects due to the non-uniform distribution of current over a large fraction of the cylinder length, which might serve to determine J _p. It is shown, adapting an argument of Hart and Swartz, that J_k should be independent of the size of the cylinder provided the ratio of length to radius is kept constant. Some of the discrepancies between theory and experiment are shown to be resolved. Cylindrical systems such as a toroid, in which the effects of ends have been removed, are briefly considered.     

Muon spin relaxation and superconducting critical currents

Effect of pinning on muon spin relaxation is discussed. The application of μSR to study of the second type superconductors are considered.     

Leakage currents in thin ferroelectric films

The basic mechanisms of leakage current components of thin lead zirconate titanate (PZT) ferroelectric films grown by the sol-gel method have been studied. Characteristic regions of current-voltage characteristics with different charge transport mechanisms have been determined. It has been shown that there is an intermediate region which separates such regions. In one of them, the leakage current depends on properties of the contact of electrodes with PZT film at low voltages; in the other, the leakage current is controlled by intrinsic properties of the PZT film bulk, and the basic mechanism of charge transport is Poole-Frenkel emission. In the intermediate region, a stepwise change in the current has been observed, which is caused by relaxing breakdown of the Schottky barrier. Time dependences of the leakage currents have been determined. It has been shown that the leakage current decreases with increasing delay time before the Schottky barrier breakdown, and the dependence becomes opposite in character after the breakdown.     

Leakage currents in ferroelectric thin films

The main mechanisms of leakage currents in thin lead zirconate titanate (PZT) ferroelectric films prepared by the sol–gel method are discussed. Four specific regions are determined in I–V dependencies. At very weak fields (10–20 kV/cm), the current falls with the voltage increase as a result of depolarization. In the low fields region (about 70–100 kV/cm), the leakage current decreases with the decrease of voltage ramp speed and its components are the ohmic and displacement currents. In the high fields region (≥130 kV/cm), the leakage current increases with the decrease of step voltage ramp in contrast to the previous case. Possible conductivity mechanisms are the Poole– Frenkel emission and hopping conduction. In the transition region between above-mentioned ones (from 80–90 to ～130 kV/cm), an abrupt unstable increase of current is observed caused by breakdown of reverse bias Schottky barrier. Depolarization currents are studied for sol–gel PZT films prepared at different preparation conditions.     

Tetracritical point and staggered vortex currents in superconducting state

A phase diagram reflecting the main features of the typical phase diagram of cuprate superconductors has been studied within the framework of the Ginzburg-Landau phenomenology in the vicinity of a tetracritical point, which appears as a result of the competition of the superconducting and insulating pairing channels. The superconducting pairing under repulsive interaction corresponds to a two-component order parameter, whose relative phase is related to the orbital antiferromagnetic insulating ordering. Under weak doping, the insulating order coexists with the superconductivity at temperatures below the superconducting phase transition temperature and is manifested as a weak pseudogap above this temperature. A part of the pseudogap region adjacent to the superconducting state corresponds to developed fluctuations of the order parameter in the form of quasi-stationary states of noncoherent superconducting pairs and can be interpreted as a strong pseudogap. As the doping level is increased, the system exhibits a phase transition from the region of coexistence of the superconductivity and the orbital antiferromagnetism to the usual superconducting state. In this state, a region of developed fluctuations of the order parameter in the form of quasi-stationary states of uncorrelated orbital circular currents exists near the phase transition line.     

Dimensionality of extremely thin superconducting films

Superconducting fluctuations above the transition temperature are strongly dependent on the dimensionality of the samples. Our experiments on extremely thin quench condensed aluminum films show transitions from zero- to one-, two- and three-dimensional behaviour at an average film thickness of 20, 50 and 100 Å respectively.     

Magnetic-flux penetration and critical currents in superconducting strips with slits

We theoretically investigate transport-current-induced magnetic-flux penetration into superconducting strip lines with slits. Even when the individual strips have no bulk pinning, geometrical barriers prevent penetration of magnetic flux into the innermost strips while flux quasistatically penetrates into the outermost slits. The critical current of strip lines with 2N slits at zero applied magnetic field is found to be enhanced by a factor of (N+1)(1/2) above that of a single strip line without slits. Under suitable conditions, a domelike flux distribution due to the geometrical barrier can appear in the individual strips even in the absence of an applied magnetic field.     

Field distortions from persistent currents in the superconducting HERA magnets

Measurements and calculations are presented on the sextupole and decapole components in the HERA dipole magnets and the 12-pole and 20-pole components in the quadrupoles. The data show a strong current dependence and a characteristic hysteresis behaviour. Good agreement is found with model calculations which are based on eddy currents in the niobium-titanium filaments of the superconducting cable.     

A fluctuation-dissipation relation and its applications to thermodynamic fluctuations in superconducting cylinders

Modifying slightly Kubo's formulation of perturbation theory to take care of the fact that generalized susceptibility may not be zero at infinite frequency, we establish, in the classical limit, a general relation between covariance and generalized susceptibility. The relation is then applied to evaluate the covariances of the magnetic flux, currents, and magnetization of a superconducting cylinder. Expressions for the spectra of magnetic flux and magnetization are also obtained.     

Quantum decay of supercurrent in thin superconducting wires

Quantum fluctuations cause a decay of the supercurrent in thin superconducting wires making them resistive even at very low temperatures. We derive a microscopic effective action formalism that goes beyond the usual TDGL approach and study quantum fluctuations of the superconducting order parameter at all temperatures belowT _C . We calculate the quantum phase slip rate in thin superconducting wires, demonstrate the importance of dissipation in a quantum phase slip process, and evaluate the resistanceR(T) of the wire. In very thin wires the effect is well observable, even at zero temperature.