Fluctuation phenomena below the superconducting transition

The fluctuation propagator for the superconducting order parameter belowT _c is derived for a gapless superconductor. The fluctuation of the order parameter consists of two distinct modes: the fluctuations of the phase and the modulus of the order parameter. The former fluctuation obeys a phononlike dispersion, while the latter fluctuation is described by a damping diffusion type equation. The present theory gives an account of the fluctuation-induced Josephson effect belowT _c observed recently by Carlson and Goldman.     

Fluctuation conductivity in the vicinity of the superconducting transition

The conductivity of the metal in the vicinity of the superconductivity transition point has been obtained. The nonlinear fluctuation effects change the temperature dependence of the conductivity in a wide range of temperatures, in which fluctuation corrections to thermodynamic quantities are still small. At comparatively strong pair breaking these effects decrease the fluctuation correction, which may exceed the conductivity of normal metal far from the transition temperature.     

Dynamical electrical conductivity in superconductors below the transition temperature

The linear electromagnetic response is calculated below the transition temperature in the dirty limit by means of the random phase approximation and fluctuation corrections. The results are related to those from the phenomenological Ginzburg-Landau equation, but do not coincide with them identically, due to the presence of a propagating mode in the two-particle correlation spectrum.     

Fluctuation conductivity in a superconducting proximity sandwich

The fluctuation conductivity above the transition temperatureT _c is calculated in a superconducting proximity sandwich containing magnetic impurities. The calculations are carried out in the framework of the Kaiser-Zuckermann theory based on the McMillan tunneling model, under the condition _S,N T _c1, where _S,N are the lifetimes of electrons associated with the tunneling process. The role of the proximity effect is to suppress the fluctuation conductivity by renormalizing the coefficients of the Aslamazov-Larkin and Maki-Thompson terms, and the third term. On the other hand, magnetic impurities affect mostly the Maki-Thompson contribution via the pair-breaking parameter, which is derived as a quantity depending on _S,N, the spin-flip lifetime, and temperature.Financial support provided by the Post-Doctoral Fellowship Commission in Science and Engineering Research Laboratory, Waseda University.     

Using ion implantation to adjust the transition temperature of superconducting films

We summarize a continuing investigation into using ion implantation to alter the transition temperature of superconducting thin films. The primary motivation for the work presented here was to study the feasibility of using magnetic ion doping to replace the bi-layer T_c control process currently used for certain cryogenic detector applications at National Institute for Standards and Technology. The results from work with various ion species implanted into aluminum, molybdenum, titanium and tungsten host films are presented.     

Electrical conductivity and transition temperature of NbN thin films

Niobium nitride thin films are grown using reactive RF sputtering technique for four different partial nitrogen pressures in argon atmosphere. The superconducting transition temperature of the films has been measured. The films exhibit a negative temperature coefficient of resistivity. The electrical characterization of the films has been carried out and the conductivity measured between room temperature and liquid nitrogen temperature. This is fitted usingT ^P law.     

Measurement of the transition temperature distribution and magneticfield profile of large superconducting films

A novel apparatus has been developed to measure the transition temperature (T_c) distribution and magnetic field profile of large superconducting films. Two techniques were used. The first one is an ac inductive method which provides a contactless measurement of T_c. The second technique employs a Hall device to measure magnetic field. Driven by two step motors, the measuring probe, either a two-coaxial-winding coil or a Hall sensor, can move over the sample on a polar plane. As the probe scans the sample step by step, various points on the sample are measured one by one. Experiments were carried out on a 30 mm diameter YBa₂Cu₃O_7-δ thin-film. The T_c distribution and the surface profile of trapped magnetic field were obtained     

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.     

Orientational order in block copolymer films zone annealed below the order--disorder transition temperature

We report measurements of rapid ordering and preferential alignment in block copolymer films zone annealed below the order-disorder transition temperature. The orientational correlation lengths measured after approximately 5 h above the glass-transition temperature ( approximately 2 microm) were an order of magnitude greater than that obtained under equivalent static annealing. The ability to rapidly process polymers with inaccessible order-disorder transition temperatures suggests zone annealing as a route toward more robust nanomanufacturing methods based on block copolymer self-assembly.     

Charge imbalance in superconducting tin films produced by a supercurrent in the presence of a temperature gradient

A pair-quasiparticle potential difference V arising from a quasiparticle charge imbalance has been measured in superconducting tin and tin-indium films along which there exist both a supercurrent I and a temperature gradient T. The voltage is proportional to I T at a given temperature, and near T _cdiverges approximately as (1 \s- t)^\s-1 for given values of I and T. Theories by Schmid and Schön and by Clarke and Tinkham are in good agreement with the temperature dependence and magnitude of V/(I T), while a theory by Beyer Nielsen et al. predicts the correct magnitude but a temperature dependence of (1 \s- t)^\s-1/2.This work was supported by the Phillips Foundation of 1958, the Danish Natural Science Research Council, and the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Science Division, U.S. Department of Energy under contract No. W-7405-ENG-48.     

Superconductor fluctuations in tunneling junctions below the transition temperature

The fluctuation current through a Josephson junction has been calculated, one side of which is a stable superconductor, the other a fluctuating one. The theoretical functions cover the frequency range 0 < 5.5. They reflect the characteristic experimental features in a consistent picture. In addition, an expression for the relaxation time of the order parameter modulus has been derived over the whole gap region for temperatures close to T _c, based on a pair-breaking mechanism.Work supported in part by the Office of Naval Research.Postdoctoral fellow of the Deutsche Forschungsgemeinschaft; on leave of absence from Technische Universität München.     

Heat capacities of granular aluminum films near the superconducting transition

The electrical conductivity and heat capacity were studied in the superconducting transition region of 1000-» thick, disordered, granular films that were evaporated onto cleaved mica substrates. The resistive transitions of films were used as thermometers in conjunction with optical heating in an ac calorimetry scheme to measure the temperature dependence of the 5 × 10^?9 J/K heat capacity of the films. Results obtained on nine samples indicated a rise in the heat capacity near the low-temperature limit of the transition region where film resistances became zero. This rise peaked in four films at values substantially greater than the estimated Bardeen-Cooper-Schrieffer jump in heat capacity and at temperatures 20–40 mK below the transition temperatures determined from a fit of the mean field theory to conductivity measurements. Quantitative comparison with theory cannot be made because transitions are broadened by film thickness variations resulting from irregular substrate topography. Results are in qualitative disagreement with the monotonic variation of the excess heat capacity calculated in the Hartree approximation. Observed peaks are also both wider and higher than those predicted by 1/n expansion and screening approximation calculations.     

Two-particle correlation functions in superconductors below the transition temperature

Order parameter fluctuations are calculated at temperatures below the critical temperature by treating pairing vibrations, density fluctuations, and coupling between them within a matrix framework. The calculations have been performed for both neutral and charged superconductors in the presence of normal impurities and pair-breaking agencies with specialization to the dirty limit. The correlation functions, evaluated for frequencies small compared to the temperature, break up into fluctuations of phase and amplitude of the order parameter. An expression for the longitudinal dielectric function is given. The two branches of gapless and gap behavior are discussed. Comparison with the diffusive time-dependent Ginzburg-Landau equations makes it possible to estimate the range of validity of the latter.     

Measurement of the Ginzburg-Landau parameter of the superconducting tin films from the supercooling field

Within the framework of Ginzburg-Landau (GL) theory we study the supercooling fields of pure tin films. We have systematically measured the supercooling field as functions of inverse thickness and temperature in both perpendicular and parallel orientations for films obtained by electrolytic deposition. By analyzing the solution of the linearized GL equation, we show that the GL parameter K of bulk material can be reliably obtained from the reduced supercooling field. The extrapolation to infinite thickness and to temperature close to the critical temperature of supercooling field allows to obtain the GL parameter of pure tin, the coherence length ξ₀, the penetration depth λ(0), the London penetration depth λ_L(0) and the zero-thermodynamic perpendicular critical field H_c(0). Our results are consistent with those obtained from supercooling fields of bulk spheres. They provide an explanation for discrepancy previously observed between values of the GL parameter in bulk samples and those deduced from superheating and supercooling fields on superconducting granules. Our results are compared with previous experimental work.     

On excess conductivity of wide superconducting films with phase slippage

Properties of wide superconducting tin films in the resistive current state with phase slippage have been studied experimentally. We have observed a region of excess conductivity on the current-voltage characteristics of the samples. Experimental results were discussed in view of the theory establishing the relationship between an interference term of the total current and excess current in weak superconductors. We derived the equation to evaluate the inelastic scattering time of superconductor τ _E using the excess current of wide films with phase slippage. Our τ _E values are in a good agreement with those obtained by other methods.     

Electron scattering and the lattice thermal conductivity of superconducting transition metal alloys

The mechanism of heat energy transport by phonon carriers which are primarily scattered by conduction electrons is re-examined for concentrated alloys in the normal and superconducting phases. The large increase in the normal state lattice thermal conductivity observed experimentally for concentrated niobium alloys, compared with the pure metal, is explained qualitatively as due to the diminished importance of scattering by d-electrons, compared with s-electrons, when the mean free path for the former becomes less than the typical phonon wavelength. Evidence is presented for the existence of a gap-less type of superconductivity in the concentrated alloys for both s and d-electrons.     

Quantum effects and the resistive transition in superconducting granular films

Static and dynamic properties of an array of Josephson junctions shunted by Ohmic resistors are discussed within a quantum Ginzburg-Landau theory. The phase diagram at zero temperature is calculated in mean field approximation. It shows that global superconductivity atT=0 is possible only if the normal-state film resistanceR _n is smaller than a critical valueR _n ^c which depends only logarithmically on the Josephson coupling and charging energies. The particular valueR _n ^c =6.5 k found in recent experiments on granular films is in reasonable agreement with estimates for these parameters. A phenomenological order parameter relaxation mechanism is introduced and the associated fluctuation-induced conductivity and diamagnetic susceptibility aboveT _c are determined. The resulting precursor conductivity does not explain the observed exponential decrease withR _n-R _n ^c of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thousless picture, is in good agreement with the experimental data.     

The cooldown process of superconducting tin films in contact with cold sapphire

Momentary current voltage characteristics of tin-tunnel junctions evaporated on an a-cut sapphire were measured during the cooldown process which starts immediately after stopping the steady-state heating from a constantan heater which was evaporated at the top of the tin diode with a SiO _x -layer in between. The measured momentary current-voltage characteristics cannot be distinguished within experimental error from thermal characteristics taken at a higher substrate temperature. Hence, at the tunnel junction, the electron system can be described at each time during the cooldown process by an electron temperatureT ₁ ^el (t). It is shown that the decay time of the electron system is far too long to be in accordance with a one-temperature model combined with the acoustic mismatch model, which has been verified in pulse-heating experiments during the heatup and steady-state time interval in a preceeding paper.¹ We observed a pure exponential decay of the electron temperature starting at the onset of superconductivity atT _C =3.72 K and ending at the bath temperature which is usually aboutT _C /2. The measured decay constant is within a 10% maximum deviation equal to the effective recombination time _eff of the injected quasiparticles, well-known from other investigations. We found the same dependence of on bath temperature, on the thickness of the tin film, and on oxygen content as was observed for _eff in earlier experiments. Simple models for the behavior of the electron and phonon system during the cooldown process are investigated to explain this unexpected decay behavior at temperatures far away from the bath temperature.     

Quasiparticle recombination time of superconducting tin films in a parallel magnetic field

The influence of a parallel magnetic field on the quasiparticle recombination time of superconducting tin tunneling junctions has been determined experimentally. The results are compared with the predictions of a theoretical model that takes into account the modification of the quasiparticle density of states by the applied magnetic field.