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In situ formed superconducting filamentary composites are of considerable interest from both theoretical and practical points of view. A number of authors1 have demonstrated that these composites can carry critical currents comparable to those of the best conventional conductors with continuous Nb3Sn or V3Ga filaments and they are also remarkably insensitive to mechanical stress or strain. Along with the powder-metallurgically processed composites,2 these new materials show realistic promise for potential practical applications and can now be produced also in large quantities.3

In this chapter we treat two contrasting examples of the longitudinal mode of quasiparticle disequilibrium. First, we treat the rather classical problem of heating effects in three-dimensional constriction weak links, which increase the Johnson noise, while reducing the critical current and energy gap. Second, we treat the more subtle nonequilibrium effects generated by a time-varying energy gap. These provide a kind of negative feedback effect which slows down the gap response time from τGL to τΔ, which may be orders of magnitude longer, and also provides a type of dynamic enhancement of superconductivity in current-driven metallic weak links.

In this paper I shall discuss how thermodynamic fluctuations affect the observable properties of superconductors, both above and below T. Although fluctuation effects can be observed also in such properties as electron tunneling, I shall restrict attention here to the basic hallmarks of superconductivity, perfect conductivity and perfect diamagnetism. First, I shall outline how the idealized properties of superconductors without fluctuations can be understood within the conceptual framework of the Ginzburg-Landau (GL) theory. Then I shall consider how fluctuations modify the idealized sharp transitions.

The magnetic field penetration depth λ of superconductors has been measured in the past by various radiofrequency and microwave techniques or by using small colloidal samples. In this paper we describe a new method, which we have successfully applied to tin, for directly measuring the temperature dependence of λ at dc and on macroscopic, oriented single crystals. The method utilizes the extremely high flux sensitivity of a SQUID magnetometer to measure the flux penetrating into a superconductor in a low (~ 1 Oe) static magnetic field. With this technique changes in λ as small as 2 A can be resolved. Moreover, flat, planar samples have been used so that both the direction of the shielding current J and the normal \(\hat{n}\) to the sample surface can be directed along well-defined crystallographic directions. The temperature dependence of λ is found to depend on both Ĵ and \(\hat{n}\). While a dependence on Ĵ has been observed previously, the dependence on \(\hat{n}\) has not. As described below, both types of anisotropy can be understood on the basis of Pippard’s nonlocal theory1 of electrodynamics.

The most elementary and familiar model for ordered magnetic systems is the so-called molecular field model, in which each spin is supposed to be acted on by a “molecular field” proportional to the magnetization or mean polarization of the other spins. This model leads to a second-order phase transition at a Curie temperature Tc above which there is no mean polarization. It gives qualitatively correct results, but is not quantitatively correct. The physical basis for the model is the exchange interaction, which introduces a coupling energy which depends on the relative spin orientations of nearby atoms. One expects the exchange coupling to fall off roughly exponentially with distance in insulating crystals, since it depends on the overlap of wavefunctions. Thus it is common to consider only nearest-neighbor coupling. Since the molecular field model essentially couples a given spin equally to all spins that participate in the average, it will give particularly bad results when each spin has only a few near neighbors.

A convenient characterization of the response of a metal to electromagnetic fields is the complex conductivity: $$ \sigma (\omega ,\text{q) = }\sigma _\text{1} (\omega ,\text{q) - i}\sigma _\text{2} (\omega ,\text{q) = }\frac{{\text{i}\omega \varepsilon \text{(}\omega \text{,q)}}} {{\text{4}\pi }} $$ (1) giving the current per unit electric field of frequency ω and wave number q. (We consider only the transverse conductivity, where E and J are perpendicular to q.) As indicated in (1), an equivalent description in terms of a complex dielectric constant E is also possible. For metals in the normal state σn(ω, q) can be calculated in the free-electron approximation by applying Fourier analysis to the well-known Chambers integral expression for the current: $$\vec J(\vec r,t) = \frac{{3\sigma _o }} {{4\pi \ell }}\int {\frac{{\vec R[\vec R\cdot\vec E(\vec r',t')]}} {{R^4 }}} \quad e - R/\ell \quad d_{\tau '}$$ (2) where \(\rm \sigma _o = ne^2\,\,\,\ l/mv_o ,\,\,\,\vec R = \vec r' - \vec r,\,t' = t - (R/v_o ),\,l\) is the mean free path, and Vo is the Fermi velocity. At ω = 0, for example, one finds σ2 = 0, and the q-dependence of σ1 is: $$ \rm \sigma _{1n} (O,\,q) = \sigma _o f(ql), $$ (3) where $$ \rm f(ql) = \frac{3}{{2q^3 l^3 }}[(1 + q^2 l^2 )\,\tan ^{ - 1} ql - ql] $$ (4) which has the asymptotic forms: $$ \rm f(ql) = \frac{3}{{2q^3 l^3 }}[(1 + q^2 l^2 )\,\tan ^{ - 1} ql - ql] $$ (4a) $$ \rm \to \left( {\frac{{3\pi }} {{4pl}}} \right)\left( {1 - \frac{4} {{\pi pl}} + \ldots } \right)(ql \to \infty ). $$ (4b)