We provide a general theoretical framework to describe the electromagnetic properties of viscous charged fluids, consisting, for example, of electrons in certain solids or plasmas. We confirm that finite viscosity leads to multiple modes of evanescent electromagnetic waves at a given frequency, one of which is characterized by a negative index of refraction, as previously discussed in a simplified model by one of the authors. In particular, we explain how optical spectroscopy can be used to probe the viscosity. We concentrate on the impact of this on the coefficients of refraction and reflection at the sample-vacuum interface. Analytical expressions are obtained relating the viscosity parameter to the reflection and transmission coefficients of light. We demonstrate that finite viscosity has the effect to decrease the reflectivity of a metallic surface, while the electromagnetic field penetrates more deeply. While on a phenomenological level there are similarities to the anomalous skin effect, the model presented here requires no particular assumptions regarding the corpuscular nature of the charge liquid. A striking consequence of the branching phenomenon into two degenerate modes is the occurrence in a half-infinite sample of oscillations of the electromagnetic field intensity as a function of distance from the interface.

The critical current density of the Nb 3 Sn superconductor is strongly dependent on the strain applied to the material. In order to investigate this dependence, it is a common practice to measure the critical current of Nb 3 Sn strands for different values of applied axial strain. In the literature, several models have been proposed to describe these experimental data in the reversible strain region. All these models are capable of fitting the measurement results in the strain region where data are collected, but tend to predict unphysical trends outside the range of data, and especially for large strain values. In this paper we present a model of a new strain function, together with the results obtained by applying the new scaling law on relevant datasets. The data analyzed consisted of the critical current measurements at 4.2 K that were carried out under applied axial strain at Durham University and the University of Geneva on different strand types. With respect to the previous models proposed, the new scaling function does not present problems at large strain values, has a lower number of fitting parameters (only two instead of three or four), and is very stable, so that, starting from few experimental points, it can estimate quite accurately the strand behavior in a strain region where there are no data. A relationship is shown between the proposed strain function and the elastic strain energy, and an analogy is drawn with the exponential form of the McMillan equation for the critical temperature.

The confinement of a superconductor in a thin film changes its Fermi-level density of states and is expected to change its critical temperature T c . Previous calculations have reported large discontinuities of T c when the chemical potential coincides with a subband edge. By solving the BCS gap equation exactly, we show that such discontinuities are artifacts and that T c is a continuous function of the film thickness. We also find that T c is reduced in thin films compared with the bulk if the confinement potential is lower than a critical value, while for stronger confinement T c increases with decreasing film thickness, reaches a maximum, and eventually drops to zero. Our numerical results are supported by several exact solutions. We finally interpret experimental data for ultrathin lead thin films in terms of a thickness-dependent effective mass.

Superconductivity develops in bulk doped SrTiO 3 and at the LaAlO 3 /SrTiO 3 interface with a dome-shaped density dependence of the critical temperature T c , despite different dimensionalities and geometries. We propose that the T c dome of LaAlO 3 /SrTiO 3 is a shape resonance due to quantum confinement of superconducting bulk SrTiO 3 . We substantiate this interpretation by comparing the exact solutions of a three-dimensional and quasi-two-dimensional two-band BCS gap equation. This comparison highlights the role of heavy bands for T c in both geometries. For bulk SrTiO 3 , we extract the density dependence of the pairing interaction from the fit to experimental data. We apply quantum confinement in a square potential well of finite depth and calculate T c in the confined configuration. We compare the calculated T c to transport experiments and provide an explanation as to why the optimal T c 's are so close to each other in two-dimensional interfaces and the three-dimensional bulk material.

We revisit the problem of a BCS superconductor in the regime where the Fermi energy is smaller than the Debye energy. This regime is relevant for low-density superconductors such as SrTiO 3 that are not in the BEC limit, as well as in the problem of "shape resonances" associated with the confinement of a three-dimensional superconductor. While the problem is not new, exact results were lacking in the low-density limit. In two dimensions, we find that the initial rise of the pairing temperature T c at low density n is nonanalytic and faster than any power of n. In three dimensions, we also find that T c is nonanalytic, but starts with zero slope at weak coupling and infinite slope at strong coupling. Self-consistent treatment of the chemical potential and energy dependence of the density of states are crucial ingredients to obtain these results. We also present exact results for multiband systems and confirm our analytical expressions by numerical simulations.