Voltage-current characteristics of a type-II superconductor placed in a transverse magnetic field

We have measured the voltageV appearing along a type-II superconducting sample carrying a longitudinal currentI in the presence of a transverse magnetic fieldH. The analysis of the nonlinear part ofV(I) curves does not verify the recent model of Sherrill and Payne. The linear part ofV(I) curves shows that the flux-flow resistivity _f is exponential inH nearH _c2, as Axt and Joiner found. We estimated the parameter =(H _c2/_n)(d_f/dH)_{H=H c2} as a function of the reduced temperature and have compared it to some of the existing theories.     

Magnetically and Thermally Modulated Microwave Absorption in Y1Ba2Cu3O7–x Single Crystal near Tc

The microwave absorption R in the Y ₁ Ba ₂ Cu ₃ O _7–x single crystals was investigated near T _c 92K and in the external magnetic field 0 < H 9kOe. A modified ESR spectrometer was used in the experiment. The method of temperature modulation, along with the usual method of magnetic-field modulation, was first applied in studying of the microwave response of these crystals. Peaks in the temperature dependencies of the signals R/H and R/T observed in the vicinity of T _c were differently shaped and shifted one with respect to another. The evolution of the peaks with variation of the magnetic field and angle between H and the c-axis was traced. It has been shown that the observed difference of the temperature dependencies of the derivatives R/H and R/T occurs due to the field-induced broadening of the superconducting transition, which is inherent in the high-T _c superconductors.     

Vortex-induced rectification in type II superconductors

We report a large rectification effect in superconducting films in a parallel magnetic field. This rectification effect is manifested in two features in current-voltage characteristics: The critical current, I_c,is found to differ by as much as 40% for negative and positive currents, and beyond I_c,the magnitude of the voltage is different for positive and negative currents, ¦V(+I)¦ ¦V(–I)¦.Furthermore, the critical current difference ¦I_c+¦ – ¦I_c–¦shows complicated behavior, changing sign as temperature and magnetic field are varied. We discuss a model based on the Bean-Livingston surface barrier and inhomogeneous bulk pinning that accounts for all observed behavior.     

On the theory of the thermoelectric effect in a superconducting bimetallic loop

The theory of the thermoelectric effect in a bimetallic superconducting contour is discussed, particularly the calculation of the magnetic flux through the contour. In a previous work ¹ we analyzed this problem and criticized Pickett's approach ² to its solution. Pickett disagrees ³ with our criticsm and with the usual expression for the magnetic flux through the contour. In this work we make some additional remarks to elucidate the correctness of this expression. The possible role of spontaneous changes of the so-called frozen-in magnetic flux through the contour is emphasized, these changes being great enough to explain the experimentally observed very large magnetic flux in a hollow superconducting toroid. It is pointed out that the effect of the spontaneous transitions is very sensitive to the circuit geometry and should be much more pronounced in the case of a hollow superconducting cylinder (or toroid) as compared with a contour of the ring type.     

The volume change at the superconducting transition of lead and aluminum

The volume change at the magnetic field-induced transition from the super-conducting to the normal state has been measured on single crystals of lead and aluminum between 0.3 K andT _c. From these data we have deduced the pressure dependence of the critical fieldH _c, of the critical temperatureT _c, and of the electronic specific heat coefficient . In lead, the results are in good agreement with theoretical calculations by Carbotte, where strong coupling effects are taken into account. We find ln / lnV=3.1±0.8, whereV is the volume. The measurements on aluminum giving ln / lnV=3±4 are consistent with results derived from thermal expansion experiments.This work was in part financially supported by the Schweizerischer Nationalfonds.     

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 Silsbee's 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 Silsbee's 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.Work performed in part in the Ames Laboratory and in part in the Argonne National Laboratory of the U.S. Atomic Energy Commission.     

Superconducting critical currents in Nb-Cu-Nb sandwiches

A preparation method is presented for Nb-Cu-Nb sandwiches for proximity-effect measurements with a large junction area of about 150×150 µm and intermediate Cu layers of thicknesses between 0.2 and 1.5 µm. The thickness of the Nb layers is about 150 µm. These samples are used to study the dependence of the superconducting critical currentI _c through the Cu layer as a function of a magnetic field applied parallel and perpendicular to the layers. Furthermore, the effects of flux lines trapped in the Nb layers on the critical currentsI _c andI _c are investigated. The results are used to discuss the influence of proximity effects in microcomposite superconductors.     

Superconductivity in bulk A15 Nb3Si under pressure

We have determined the effect of hydrostatic pressureP on the superconducting transition temperatureT _c of bulk, A15 Nb₃Si. For 0P20 kbar (2 GPa),T _c decrease linearly with increasing pressure at a rate T _c/P=–2.67×10^–5 K/bar. From an estimate of T _c/P obtained using recent band structure calculations for the density-of-electronic-states change as a function of lattice parameter in Nb₃Si, we conclude that the pressure dependence of the electron-phonon interaction primarily determines T _c/P.Work performed under the auspices of the U.S. DOE.     

Kinetics of the destruction of type-I superconductivity by a current in a wire submitted to a longitudinal magnetic field

The dynamics of the destruction of type-I superconductivity are studied for the case of a cylindrical wire submitted both to a current and to a longitudinal magnetic fieldH . During the penetration of the flux into the cylinder, the component of the magnetic induction parallel to the axis increases as one approaches the axis: this is a consequence of the special form of Ampère's law in the intermediate state. The relation of this phenomenon with the paramagnetic effect is discussed.Work partially supported by the Fonds National Suisse de la Recherche Scientifique.     

Possibility of higher order critical fields in superconducting rings

The behavior of a small superconducting ring or hollow cylinder in an axial magnetic field is studied using the nonlinear Ginzburg-Landau equations. We find that, if the radius of the cylinder is smaller than half the superconducting coherence length (T), a periodic alternation between the superconducting and the normal state occurs as the magnetic field is increased. This defines higher order critical magnetic fields for vanishing and reentrant superconductivity.     

Critical fields and generalized Ginzburg-Landau parameters for Mo-Re alloys containing paramagnetic impurities

We have investigated the temperature dependence of the upper critical fieldH _c2 and the thermodynamical fieldH _c for superconducting Mo-Re alloys containing magnetic impurities. In addition, the temperature dependence of the Ginzburg-Landau parameters ₁(T) and ₂(T) has been determined by measuring the magnetization and the specific heat. Our findings are compared with the theory of Fulde and Maki. In agreement with theory, our measurements show that the two pair-breaking mechanisms involved (magnetic field and magnetic impurities) are nonadditive if one departs from the linearized Ginzburg-Landau equation.     

Flux line density gradient in the mixed state of type II superconductors

The value of the critical current for a type II (1) superconducting slab placed in a magnetic fieldH _e (H _c1H _e H _c2) parallel to the sample surface and with a currentI flowing perpendicular to the magnetic field is obtained. This critical current depends on the characteristic length of the mixed state . The critical state equation for a simple system with pinning is given. The equation relating the length with the Campbell pinning length is obtained in the special case . A formula for the surface impedance of the mixed state is given.     

Granular superconductors and their intrinsic and extrinsic surface impedance

High-frequency experiments depend sensitively on homogeneous and inhomogeneous defects in the normal and superconducting state. As homogeneous effects, the intrinsic scattering time is of great theoretical importance above 0.1 THz in the surface impedanceZ. Of practical importance are the planar defects, the weak links (WL), which interrupt the rf shielding currents and thus enhanceZ _eff. In the superconducting state, the Josephson currentj _cJ crosses the WL in parallel with the normal, leakage currentj _bl . The latter explains the observed, finite rf residual lossesR _res(T0) quantitatively and as a function of material parameters, temperatureT, fieldH, and frequency for Nb, NbN, and cuprate superconductors. With increasing field,Z deteriorates likeH ² up toH _cIJ, where Josephson fluxons (JF) penetrate into the WL yieldingZ H. Above H _cIJ 0.1–10 mT, JF dynamics dominatesZ with hysteresis losses and reactive components. The nonlinear JF effects are enforced by thin-film edge enhancements limiting the performance of various devices by enhanced dissipation, reactance, and flux noise. A method is presented which is able to separate electron dynamics at the WL from their strength and distribution.     

Reversible Magnetic Behavior of Superconductors Forced by a Small Transverse AC Magnetic Field

Recently it was shown that with thin superconductors placed in a transverse dc magnetic field, the application of a small ac magnetic field perpendicular to the dc field causes rapid relaxation of the irreversible magnetization. We show here that for a thin superconducting strip in a transverse dc field the application of a weak ac field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the walking motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors with pinning. Some recent experiments are discussed.     

Magnetic field effects in thick proximity-induced superconductors

Low-field magnetic screening and breakdown fields have been measured in thick proximity-induced superconducting copper by means of dc magnetization and ac susceptibility in the temperature range 10 to 0.005 K. From the thickness and temperature dependence of the breakdown field the Cooper pair penetration depth in copper is obtained. This value isK _N ^–1 =0.6/T m, withT in kelvins. No saturation effects were observed in the screening length , the breakdown fieldH _b, or the supercooled fieldH _sc down to the lowest temperatures.     

Superconductivity effects near the metal-insulator transition in granular indium films

The paper reports on an investigation of the electric resistance as a function of temperatureT, magnetic fieldH, and applied voltageV in granular indium films when approaching the metal-insulator transition (MIT) due to increased thickness of the oxide layers between granules. The dependences are shown to be governed atT5 K by competition of the hopping conductivity and the Josephson tunneling of electrons, sometimes giving rise to a resistance minimum inR(T) associated with superconductivity. It was also found that even when the intergranular Josephson tunneling is totally suppressed, transition of granules to the superconducting state influences essentially the dependencesR(T, H), changing the functional form ofR(T) and resulting in anomalously high negative magnetoresistance. This is shown to stem from the change of the character of activated electron tunneling as the granules become superconducting.     

Orbital glass in HTSC: a new state of condensed matter

We show that in granular high-temperature superconductors (HTSC) at small magnetic fields the Meissner effect may disappear. A possible explanation for this effect may be related to the existence of special loops of Josephson junctions with positive and negative Josephson couplings. These loops have been observed in a large number of experiments in granular HTSC. On the Josephson loop with an odd number of negative couplings a spontaneous orbital moment is created. The new state of the HTSC with orbital moments, which indeed is a new state of Condensed Matter, is characterized by the coexistence of the orbital paramagnetic state with the superconducting state.If the Coulomb blockade is taken into account, the critical fieldH _c0 of the transition into the new orbital glass state increases. The new state exists only for magnetic fieldsHH _c0. We have estimated the value of orbital moments and also the influence of the charging energy on orbital magnetism.We show that the critical fieldH _c0 of the orbital paramagnetic glass transition is inversely proportional to the surface areaS of an average loop of Josephson junctions in granular HTSC or the cross-sectional area of an average grainS: H _c0 H₀/S, where ₀ is the elementary flux quantum. Recent experiments demonstrate that at small magnetic fields (0.1–2 Oe) the Meissner effect in granular HTSC (2212-Bi compound) and in other compounds disappears. If we insert in our formula an appropriate value for the cross-section of an average grain, we obtainH _c0 of the order of 2 Oe. This confirms the prediction of our theory on the existence of a new critical fieldH _c0 , which we call the orbital glass critical field.Invited talk at the Physical Society of Finland, Lahti, Finland, March 20, 1992.     

Experimental evaluation of the nonlinear surface resistance of YBa2Cu3O7?x step-edge grain boundary Josephson junctions

The temperature, microwave current, and dc magnetic field dependencies of the effective surface resistanceR _s of YBa₂Cu₃O_7–x grain boundary Josephson junctions have been investigated at 6 GHz. The junctions were prepared on stepped LaAlO₃ substrates and incorporated into tapered linear half-wavelength microstrip resonators. The characteristic parameters of the heterogeneous resonator were analyzed theoretically considering the junction as a lumped element of complex impedance. The microwave properties of the junction could then be extracted and related to their characteristic dc transport properties. The critical currentI _c of the junction was found to limit the linear power dissipation in the superconducting strip. At microwave currents aboveI _c , highly nonlinear microwave losses occurred, which displayed a characteristic magnetic field modulation. At even higher currents,R _s saturated at a level corresponding to the normal resistanceR _n of the junction.