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.

Abstract: This Letter presents a generalized Ginzburg-Landau equation for the superconducting order parameter which includes the terms resulting from the confining interaction associated with the specimen boundary. While the original Ginzburg-Landau theory had been developed for a bulk superconductor, this generalization is meant for study of a meso-superconductor. (C) 2004 Elsevier B.V. All rights reserved.

Abstract: Based on the Gor'kov formalism for a clean s-wave superconductor, we develop an extended version of the single-band Ginzburg-Landau (GL) theory by means of a systematic expansion in the deviation from the critical temperature T(c), i.e., tau = 1 – T/T(c). We calculate different contributions to the order parameter and the magnetic field: the leading contributions (proportional to tau(1/2) in the order parameter and. t in the magnetic field) are controlled by the standard GL theory, while the next-to-leading terms (proportional to tau(3/2) in the gap and proportional to tau(2) in the magnetic field) constitute the extended GL (EGL) approach. We derive the free-energy functional for the extended formalism and the corresponding expression for the current density. To illustrate the usefulness of our formalism, we calculate, in a semianalytical form, the temperature-dependent correction to the GL parameter at which the surface energy becomes zero, and analytically, the temperature dependence of the thermodynamic critical field. We demonstrate that the EGL formalism is not just a mathematical extension to the theory: variations of both the gap and the thermodynamic critical field with temperature calculated within the EGL theory are found in very good agreement with the full BCS results down to low temperatures, which dramatically improves the applicability of the formalism compared to its standard predecessor.

Abstract: Superconductors, ideally diamagnetic when in the Meissner state, can also exhibit paramagnetic behavior due to trapped magnetic flux. In the absence of pinning such paramagnetic response is weak, and ceases with increasing sample thickness. Here we show that in multiband superconductors paramagnetic response can be observed even in slab geometries, and can be far larger than any previous estimate – even multiply larger than the diamagnetic Meissner response for the same applied magnetic field. We link the appearance of this giant paramagnetic response to the broad crossover between conventional Type-I and Type-II superconductors, where Abrikosov vortices interact non-monotonically and multibody effects become important, causing unique flux configurations and their locking in the presence of surfaces.

Abstract: Quantization of the transverse electron motion in high-quality superconducting metallic nanowires and nanofilms results in the formation of well-distinguished single-electron subbands. They shift in energy with changing thickness, which is known to cause quantum-size superconducting oscillations. The formation of multiple subbands results in a multigap structure induced by the interplay between quantum confinement and Andreev mechanism. We investigate multisubband superconductivity in a hollow nanocylinder by numerically solving the Bogoliubov-de Gennes equations. When changing the inner radius and thickness of the hollow nanocylinder, we find a crossover from an irregular pattern of quantum-size superconducting oscillations, typical of nanowires, to an almost regular regime, specific for superconducting nanofilms. At this crossover the multigap structure becomes degenerate. The ratio of the critical temperature to the energy gap increases and approaches its bulk value while being reduced by 20-30% due to Andreev-type states driven by quantum confinement in the irregular regime.

Abstract: It is well known that the formation of discrete electron levels strongly influences the pairing in metallic nanograins. Here, we focus on another effect of quantum confinement in superconducting grains that was not studied previously, i.e., spatially nonuniform pairing. This effect is very significant when single-electron levels form bunches and/or a kind of shell structure. We find that, in highly symmetric grains, the order parameter can exhibit variations with position by an order of magnitude. Nonuniform pairing is closely related to a quantum-confinement-induced modification of the pairing-interaction matrix elements and size-dependent pinning of the chemical potential to groups of degenerate or nearly degenerate levels. For illustrative purposes, we consider spherical metallic nanograins and also rectangular shapes. We show that the relevant matrix elements are, as a rule, enhanced in the presence of quantum confinement, which favors spatial variations of the order parameter, compensating the corresponding energy cost. The size-dependent pinning of the chemical potential further increases the spatial variation of the pair condensate. The role of nonuniform pairing is smaller in less symmetric confining geometries and/or in the presence of disorder. However, it always remains of importance when the energy spacing between discrete electron levels δ is approaching the scale of the bulk gap ΔB, i.e., δ>0.10.2 ΔB.

Abstract: Recently fabricated single-crystalline atomically flat metallic nanofilms are in fact quantum-engineered multiband superconductors. Here the multiband structure is dictated by the nanofilm thickness through the size quantization of the electron motion perpendicular to the nanofilm. This opens the unique possibility to explore superconductivity in well-controlled multi-band systems. However, a serious obstacle is the absence of a convenient and manageable theoretical tool to access new physical phenomena in such quasi-two-dimensional systems, including interplay of quantum confinement and fluctuations. Here we cover this gap and construct the appropriate multiband Ginzburg-Landau functional for nano-thin superconductors. Copyright (C) EPLA, 2013

Abstract: The effect of a parallel magnetic field on the orbital motion of electrons in high-quality superconducting nanowires resulting in a superconductor-to-normal transition which occurs through a cascade of jumps in the order parameter as a function of the magnetic field. Such cascades originate from the transverse size quantization that splits the conduction band into a series of subbands. Here, based on a numerical solution of the Bogoliubov-de Gennes equations for a hollow nanocylinder, we investigate how the quantum-size cascades depend on the confining geometry, i.e., by changing the cylinder radius R and its thickness d we cover the range from the nanowire-like to the nanofilm-like regime. The cascades are shown to become much less pronounced when increasing R/d, i.e., when the nanofilm-like regime is approached. When the temperature is non-zero they are thermally smoothed. This includes the spin-magnetic-field interaction which reduces the critical (depairing) parallel magnetic field H-c,H-parallel to but does not have any qualitative effect on the quantum cascades. From our calculations it is seen that the paramagnetic limiting field H-par significantly exceeds H-c,H-parallel to even in extremely narrow nanocylinders, i.e., when R, d are down to a few nanometers, and H-c,H-parallel to is only about 10% larger when switching-off the spin-magnetic-field interaction in this case. Both characteristic fields, H-c,H-parallel to and H-par, exhibit pronounced quantum-size oscillations. We demonstrate that the quantum cascades and the quantum-size oscillations survive in the presence of surface roughness.