Abstract: We investigate how the interplay of quantum confinement and particle number-parity fluctuations affects superconducting correlations in ultra-small metallic grains. Using the number-parity projected BCS formalism we calculate the critical temperature and the excitation gap as a function of the grain size for grains with even and odd number of confined carriers. We show that the experimentally observed anomalous increase of the coupling ratio ΔE/kBTc with decreasing superconducting grain size can be attributed to an enhancement of the number-parity fluctuations in ultra-small grains.

Abstract: Quantum confinement of the transverse electron motion is the major effect governing the superconducting properties of high-quality metallic nanofilms, leading to a nonuniform transverse distribution of the superconducting condensate. In this case the order parameter can exhibit significant local enhancements due to these quantum-size effects and, consequently, quasiparticles have lower energies when they avoid the local enhancements of the pair condensate. Such excitations can be considered as new Andreev-type quasiparticles but now induced by quantum confinement. By numerically solving the Bogoliubovde Gennes equations and using Anderson's approximate solution to these equations, we: (a) formulate a criterion for such new Andreev-type states (NATS) and (b) study their effect on the superconducting characteristics in metallic nanofilms. We also argue that nanofilms made of low-carrier-density materials, e.g., of superconducting semiconductors, can be a more optimal choice for the observations of NATS and other quantum-size superconducting effects.

Abstract: From a numerical solution of the Bogoliubov-de Gennes equations, we investigate an interplay of the transverse discrete modes with a longitudinal supercurrent in a metallic cylindrical superconducting nanowire. The superconductor-to-normal transition induced by a longitudinal superflow of electrons is found to occur as a cascade of jumps in the order parameter (supercurrent and superfluid density) as a function of the superfluid velocity for diameters d<1015 nm (for Al parameters) and sufficiently low temperatures T<0.30.4Tc, with Tc the critical temperature. When approaching Tc, the jumps are smoothed into steplike but continuous drops. A similar picture occurs for d>1520 nm. Only when the diameter exceeds 5070 nm the quantum-size cascades are fully washed out, and we arrive at the mesoscopic regime. Below this regime the critical current density jc exhibits the quantum-size oscillations with pronounced resonant enhancements: the smaller the diameter, the more significant is the enhancement. Thickness fluctuations of real samples will smooth out such oscillations into an overall growth of jc with decreasing nanowire diameter.

Abstract: Recent progress in materials synthesis enabled fabrication of superconducting atomically flat single-crystalline metallic nanofilms with thicknesses down to a few monolayers. Interest in such nano-thin systems is attracted by the dimensional 3D-2D crossover in their coherent properties which occurs with decreasing the film thickness. The first fundamental aspect of this crossover is dictated by the Mermin-Wagner-Hohenberg theorem and concerns frustration of the long-range order due to superconductive fluctuations and the possibility to track its impact with an unprecedented level of control. The second important aspect is related to the Fabri-Perot modes of the electronic motion strongly bound in the direction perpendicular to the nanofilm. The formation of such modes results in a pronounced multiband structure that changes with the nanofilm thickness and affects both the mean-field behavior and superconductive fluctuations. Though the subject is very rich in physics, it is scarcely investigated to date. The main obstacle is that there are no manageable models to study a complex magnetic response in this case. Full microscopic consideration is rather time consuming, if practicable at all, while the standard Ginzburg-Landau theory is not applicable. In the present work we review the main achievements in the subject to date, and construct and justify an efficient multiband mean-field formalism which allows for numerical and even analytical treatment of nano-thin superconductors in applied magnetic fields.

Abstract: Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow variations in the single-particle density of states driven by the size quantization. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size coherent effects, overlooked previously. The many-body physics is revealed here in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. The single-particle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasi-free dispersion. This results in the formation of a series of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEC-like components.