The effects of thermodynamic fluctuations near superconducting phase transitions are reviewed. Above Tc, fluctuations towards the superconducting state lead to the appearance of excess conductivity, diamagnetism, specific heat, and tunnelling currents. Below Tc, fluctuations towards the normal state lead to the appearance of resistance in thin wires and the breakdown of fluxoid quantization in small rings. These effects are generally small, but they can be measured experimentally, particularly in superconducting samples of reduced dimensionality (on the scale of the Ginzburg-Landau coherence length) such as thin films, whisker crystals, and powders. These phenomena are explained using Ginzburg-Landau theory (the salient features of which are developed concurrently), and the current status of theoretical and experimental studies of these effects is surveyed.

https://iopscience.iop.org/article/10.1088/0034-4885/38/9/001/pdf

Fluctuations near superconducting phase transitions

Superconductivity and ferromagnetic ordering are two antagonistic types of ordering, and their mutual influence leads to many interesting phenomena which have been studied recently in ternary compounds. Theoretical analysis of ferromagnetic materials which are type II superconductors near the superconducting transition point T cl shows that they become type I near the magnetic transition point T M. The proposed theory constructed for the case T M « T cl predicts the formation of a transverse domain-like (DS phase) magnetic structure below T M. The electronic spectrum appears to be gapless in the DS phase of clean compounds with a re-entrant transition. The change from type II to type I behaviour as the sample is cooled to T M has been observed in ErRh4B4. Experimental data for HoMo6S8, HoMo6Se8 and ErRh4B4 give evidence for the coexistence of super-conductivity and non-uniform magnetic ordering below T M. Mutual influence of superconducting and magnetic orderings is also studied.

Coexistence of superconductivity and magnetism theoretical predictions and experimental results

Granular Metal Films

Thin films provide an ideal means for studying the role of spin paramagnetism in the theory of superconductivity. A review is given of the theoretical and experimental work available until now with respect to this problem. It includes a study of the excitation spectrum of thin films in a parallel magnetic field and the experimental evidence of Zeeman splitting of superconducting quasiparticles. The role of spin-orbit interaction is discussed in detail. The application of spin selective tunnelling is shown. Furthermore, it includes a study of the order of phase transition between the normal state and the paramagnetically limited superconducting state. A detailed discussion is given of the generalized Ginzburg-Landau equation including numerical evaluations. The applicability of Tinkham's formula is discussed, which is relevant for the determination of critical fields of arbitrary orientations to the film. Finally, account is given of the work which deals with the influence of spin paramagnetism on...

High field superconductivity in thin films

The low-temperature heat capacities of transition metals and alloys were reviewed by Heiniger, Bucher, and Muller1 in 1966, with particular emphasis on the dependence of the electronic heat capacity on the number of conduction electrons. Nuclear contributions to the heat capacity of metals and alloys have been reviewed recently by Lounasmaa.2 The most recent general review of the low-temperature heat capacities of metals, however, was that by Keesom and Pearlman3 in 1956. Since that time there have been important advances in experimental techniques and also in theory related to certain of the heat capacity contributions.

Low-temperature heat capacity of metals

The electrical conductivity above the transition temperatureT

 c
 due to fluctuations of the superconducting order parameter has been measured in aluminum films in the presence of a magnetic field (parallel and perpendicular to the film surface), as well as in the absence of a magnetic field. It has been found, in particular from the results in a perpendicular magnetic field, that the Aslamazov-Larkin theory (AL) and its extension can be applied for temperatures close toT

 c
 . A deviation from the theoretical linear relation (AL) σn/σ′(T) ∼ ln(T/T

 c
 ) in zero and parallel field might be explained in terms of the Maki-Thompson model (MT), which is consistent with previous experiments in Al films. However, the transition width due to fluctuations in a perpendicular magnetic field is not always enhanced, contrary to the prediction of the MT model. Even in the cases in which they are enhanced, the transition width is smaller than the value predicted by the MT model.

Magnetic field effects on the electrical conductivity due to flucíuations of the superconducting order parameter above T c

The GLAG theory predicts that the value of the specific heatC

 M
 in the mixed state just below the transition to the normal state, is a function of the Ginzburg—Landau (GL) parameter κ, even for vanishingly small magnetic fields(T≈T

 c
 ).C

 M
 is thus different from the specific heatC

 S
 in the pure superconducting state(H=0) for all κ except κ≅1.9. Experimental results of the authors generally confirm this paradoxical prediction which is not in contradiction with the thermodynamics of phase transitions. To experimentally clarify this behavior close toT

 c
 , Nb80Mo20(κ≅4) and Pb98In2(κ≅0.8) specimens are studied in fields much smaller than those usually applied (down to17 Oe). A new method for measuring specific heat in decreasing as well as increasing temperature is introduced. Very good agreement with the theory is found for fields higher than ∼120 Oe while a deviation is observed close toT

 c
 for lower fields where values of the Abrikosov lattice parameter would become larger than 1 µ. The sense and the magnitude of the deviation are such thatC

 M
 andC

 S
 would be equal for fields of 20 Oe and below. Possible explanations are discussed. It is suggested that a fundamental modification of the vortex state structure occurs in small fields close toT

 c
 .

Specific heat of type-II superconductors in magnetic fields near T c

Kinetics of the destruction of type I superconductivity by a current

An experimental investigation of the kinetics of the destruction of superconductivity by rectangular current pulses was made on cylindrical Sn and In wires of different purities and diameters. The study was based on the observation of the variation of the voltage along the sample during the transition. As shown by Rothen and Bestgen, only the timet
1 between the beginning of the transition and the onset of the intermediate state can be determined with this method. The results show that if the currentI is sufficiently larger than the critical currentI

 c
 (typicallyI⪞1.15I

 c
 ), then both shape of the voltage pulses and the transition times agree well with the predictions of the electromagnetic theory of these authors. The transition is, in that case, controlled by the electromagnetic damping associated with the penetration into the normal material of the magnetic field due to the current. IfI is close to
 c
 , then the transition is much slower than predicted by the theory and seems to be essentially governed by thermal effects, i.e., absorption of latent heat, generation of Joule heat, and heat exchange with the helium bath; a small influence of superheating is observed in indium samples.

L. Rinderer

Papers

Magnetic field effects on the electrical conductivity due to flucíuations of the superconducting order parameter above T c

Specific heat of type-II superconductors in magnetic fields near T c

Kinetics of the destruction of type I superconductivity by a current

Kinetics of the current-induced phase transition in type-I superconductors

Entropy of vortices in a highly reversible type II superconducting alloy