Patterns of magnetic flux penetration in superconducting films

Intermediate-state magnetic flux patterns have been observed in thin superconducting films of tin, lead, and indium in perpendicular applied fields of 0.1–100 Oe. The spatial variation in flux density was measured very close to the film with a high-resolution Hall probe which could be scanned in a plane parallel to the surface of the film. The patterns appear to contain both laminar and round normal regions, with the latter predominant. A model for the intermediate state has been developed in which the normal regions are macroscopic flux spots. Experimental results for the number density of these flux spots in 1.1–6.3--thick indium samples are in good agreement with the temperature, field, and thickness dependences of our model; indium samples thinner than 1 µ appear to enter the mixed state. In tin and lead, however, the flux patterns are strongly influenced by flux pinning. Appearance of the flux pattern at the critical field or temperature has been observed and correlated with distinctive features in the resistive transition. The extent of flux penetration into the sample was determined from measurement of the average field and compared for various field-temperature paths to the intermediate state. With the applied field reduced to zero, the magnetic field outside a current-carrying superconducting strip has been measured and indicates that the current distribution within the strip is consistent with the form predicted by Bowers.Supported in part by the NSF, ONR, and ARPA.     

Dendritic flux avalanches in superconducting Nb3Sn films

The penetration of magnetic flux into a thin superconducting film of Nb₃Sn with critical temperature 17.8 K and critical current density 6 MA/cm² was visualized using magneto-optical imaging. Below 8 K an avalanche-like flux penetration in form of big and branching dendritic structures was observed in response to increasing perpendicular applied field. When a growing dendritic branch meets a linear defect in the film, several scenarios were observed: the branch can turn and propagate along the defect, continue propagation right through it, or “tunnel” along a flux-filled defect and continue growth from its other end. The avalanches manifest themselves in numerous small and random jumps found in the magnetization curve.     

Anomalous temperature dependence of the quasiparticle-injection-induced voltage onset in superconducting lead films

The large quasiparticle injection through a tunnel barrier is studied, in particular when the bias tunnel voltage is close to the gap edge. It is shown that the quasiparticle-injection-induced voltage threshold in a superconducting lead film has an anomalous temperature dependence above T. The effect cannot be accounted for by simple heating. Below T, a first-order transition of the lead film is observed. A possible explanation based on a nonequilibrium model is given.     

Nonequilibrium gap instability and phase transition under intense tunnel injection in superconducting lead films

We report on lead energy gap measurements made under intense tunnel current injection near the gap edge at various temperatures in terms of the differential tunnel resistance at zero bias voltage using the double-junction configuration. It is shown that the behavior is significantly different below T and above T . For T < T , a first-order transition occurs and the result is close to the prediction by the ^* model, although the estimated phonon trapping factor may be large. For T > T , an instability similar to that of Chang and Scalapino is observed. The gap reduction behavior, however, is complicated, and cannot be interpreted in terms of present theories. In addition, a new structure which indicates an abrupt enhancement of the gap is observed.     

A superconducting magnetic flux compressor

The design and operation of a mechanical superconducting flux compressor is described. The compressor is constructed of movable interleaved plates, rather like a variable capacitor. Increasing the overlap of the two sets of plates decreases the size of a hole in which magnetic flux is trapped, thus increasing the flux density.     

Experiments on flux jumps in superconducting tapes

Experimental results are reported on flux jumps measured by means of search coils on a short sample superconducting tape in an increasing field perpendicular to its surface. The superconducting material, the stabilizing copper thickness, the cooling condition, and the transport current have been varied during the tests. A small coil wound with a superconducting tape was also tested in a increasing perpendicular field. The flux jumps measured here are classified on the basis of their characteristics observed in the experiment.     

Nonlinear dynamics in superconducting films

The theory of Halperin and Nelson describes the linear response of a superconducting film close to the Kosterlitz-Thouless transition to an ac field. We have extended this theory so as to describe the non-linear response in lowest order in the driving field. Two effects are predicted: the response at the driving frequency becomes non-linear, and odd harmonics are generated. We calculate explicitly the size and temperature dependence of these effects when the response is generated and detected by an identical pair of coils placed symmetrically either side of the film.     

Resistive transition in superconducting films

The consequences of a vortex unbinding picture of two-dimensional superconductivity are worked out. Although there is no true finite-temperature phase transition, dirty superconducting films should display anomalous behavior below the BCS transition temperature and above an effective Kosterlitz-Thouless vortex unbinding temperature. In particular, both the conductivity and fluctuation diamagnetism behave like ₊ ² in this regime, where ₊ is the correlation length calculated by Kosterlitz, _{+ c} exp (B/T – T _c)^1/2. We estimate _c, B, and the vortex unbinding temperature, and determine the nonlinear resistivity below T _c. A recent theory of vortex dynamics, together with a time-dependent Ginzburg-Landau theory, lead to a determination of the frequency-dependent conductivity.This work was supported by the National Science Foundation under Grant No. DMR 77-10210.     

High-Tc superconducting thin films

This review describes recent advances in thin film studies of high-T_c superconducting cuprates. Emphasis is placed on epitaxial thin film growth technologies for LnBa₂Cu₃O_x (Ln = Y, Eu) cuprates, and on microwave device applications. An exciting area of this research involves epitaxial multilayer structures, such as a superconductor/insulator/superconductor (SIS) combination, and so preliminary results on SIS fabrication are also described.     

Quantum fluctuations in continuous superconducting films

Motivated by recent experiments on ultrathin continuous superconducting films, we study the dependence ofT _c and (for zero temperatures) on the film thicknessd. Using field-theoretical methods, we express the Coulomb interaction in terms of a fluctuating potential, and the fluctuation correction to the free energy (in one-loop approximation) is determined. Based on the standard dirty-limit expressions for the response functions, we findT _c and by a numerical investigation of the gap equation. Generally, we find that the decrease ofT _c and vs.d ^–1 is quite similar, but depends sensitively on both the large-wave-vector cut-off and the strength of the interaction. In particular, however, for a strong interaction (Coulomb interaction), the order parameter is more strongly suppressed than the critical temperature, which is due to long-wavelength fluctuations of the phase and the potential.     

Weak-link behavior in superconducting thick films

The surface impedance of melt-processed thick films of YBa₂Cu₃O_7–x on yttria-stabilized zirconia substrates has been measured as a function of temperature over the frequency range 9–18 GHz using an endwall replacement technique. The temperature dependence of both the penetration depth and the surface resistance of thisp-type cuprate system can be described within a two-gap weak-link model. The surface resistance scaled to 10 GHz by the observedf ² frequency dependence gives a value of 1.8 m at 77 K, which compares favorably with the lowest reported values for thick films of this material at microwave frequencies. Trends in material processing indicate that increasing the grain size would further decrease the surface resistance at microwave frequencies.     

Dynamics of vortices in current-carrying superconducting films

We study analytically and numerically the dynamics of vortices in current-carrying quasi-two dimensional superconducting films using the generalized time-dependent Ginzburg-Landau equations. The values of the mobility are determined analytically in the thin-film limit. The results are in quantitative agreement with numerical simulations.     

Interaction of flux tubes in a type I superconductor

The repulsive interaction between multiquantum flux tubes in type I superconducting lead films has been studied magnetooptically. Two or three flux tubes were trapped in a long and narrow region of slightly reduced film thickness, and the flux tube positions were recorded as a function of an applied Lorentz force pressing the tubes against each other. At distances larger than about the flux tube diameter our results agree well with the magnetic monopole model, which only takes into account the magnetic stray field outside the superconducting film. At smaller distances deviations from the monopole model occur due to the influence of the cross-sectional shape of the flux tubes and of the wall of the tubes upon the energy of the flux tube configuration. These influences have been taken into account by means of a subdivision model in which the flux-containing region of each tube is divided into a large number of flux portions each of which is approximated again by a magnetic monopole. For sufficiently high compression due to the Lorentz force, we have observed fusion of two individual flux tubes. Upon reduction of the Lorentz force, the fused flux tubes separate again. The process of fusion and separation shows distinct hysteresis. This behavior is also well explained by our subdivision model.     

Field enhancement in superconducting solenoids by holmium flux concentrators

The magnetic field strength in the bore of a 13 T superconducting solenoid was enhanced to 16 T in the 5.5 mm gap between two cylindrical holmium flux concentrators. This method is an economic way of extending the field region for measuring critical data of superconducting materials. The measured dependence of the gap field on coil current was reproduced in computer calculations by fitting the magnetization curve of holmium at 4.2 K. This curve may be used for optimizing the geometry of holmium flux concentrators at 4.2 K.     

Pair-field susceptibility of superconducting Al-Er films

Measurements of the imaginary part of the pair-field susceptibility have been carried out on dirty-limit superconducting Al films doped with Er impurities at temperatures within 20% of the critical temperature T _c. These studies are the first measurements of (, k) as a function of the pair-breaking parameter . Samples exhibiting values of up to 0.1 were studied. At temperatures above T _c the diffusive time-dependent Ginzburg-Landau equation for order-parameter fluctuations was found to be valid in the presence of pair-breaking, with the Ginzburg-Landau time an increasing function of the pair-breaking, in quantitative agreement with theory. The characteristic frequencies of the transverse and longitudinal modes of the order parameter disequilibrium were determined from the measurements of (, k) below T _c by fitting to a functional form which exhibits the essential features of the most detailed theories, in particular those of Orbach and Entin-Wohlman, Dinter, and Schön and Ambegaokar, The propagating charge-imbalance wave was found to be overdamped for large values of , consistent with the theory of the transverse mode in the presence of finite pair-breaking. The peak in the excess current found near the gap voltage appears to be due to a resonance in the longitudinal mode pair-field susceptibility and not the result of single-particle tunneling as previously suggested by imanek and Hayward. The width of this resonance as derived by Schön and Ambegaokar for the gap regime is equal to the reciprocal of the spin-flip scattering time. The other characteristic feature of the pair-field susceptibility is the peak associated with the longitudinal mode, which occurs at a frequency which is a measure of the relaxation of the amplitude of the order parameter. Dinter's theory, in particular, describes the dependence of the width of this peak on the pair-breaking parameter .Support for this research was initially provided by the Department of Energy and later by the NSF under Grant DMR-8006959. The Office of Naval Research provided He gas used in these experiments.     

Lithographic patterning of superconducting YBCO films

Microbridges of YBa₂Cu₃O₇ thin films have been fabricated by conventional photolithography and wet chemical etching using EDTA, and by the lift-off lithography technique. The variation of etch rate with etch time, etchant temperature, and post-deposition sintering temperature has been studied. It has been shown that both techniques are useful for film patterning. However, an additional sintering step is necessary for the chemically etched sample to regain the original film properties. An order of increase in critical current density is observed for the patterned film.     

Diffusive instability in optically excited superconducting films

We show that there is a large class of quasiparticle distributions, qualitatively similar to those predicted for optically excited superconductors, that may lead to a spatial instability driven by quasiparticle diffusion. The resultant inhomogeneous state would consist of distinct regions characterized by a length scale (quasiparticle diffusion length) and different energy gaps. We discuss the dynamics of this inhomogeneous state, and its experimental implications.Work supported in part by JSEP, ONR, and NSF.