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: 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.

Abstract: Quantum confinement of the perpendicular motion of electrons in single-crystalline metallic superconducting nanofilms splits the conduction band into a series of single-electron subbands. A distinctive feature of such a nanoscale multi-band superconductor is that the energetic position of each subband can vary significantly with changing nanofilm thickness, substrate material, protective cover and other details of the fabrication process. It can occur that the bottom of one of the available subbands is situated in the vicinity of the Fermi level. We demonstrate that the character of the superconducting pairing in such a subband changes dramatically and exhibits a clear molecule-like trend, which is very similar to the well-known crossover from the Bardeen-Cooper-Schrieffer regime to Bose-Einstein condensation (BCS-BEC) observed in trapped ultracold fermions. For Pb nanofilms with thicknesses of 4 and 5 monolayers (MLs) this will lead to a spectacular scenario: up to half of all the Cooper pairs nearly collapse, shrinking in the lateral size (parallel to the nanofilm) down to a few nanometers. As a result, the superconducting condensate will be a coherent mixture of almost molecule-like fermionic pairs with ordinary, extended Cooper pairs.

Abstract: Superconducting correlations in an isolated metallic grain are governed by the interplay between two energy scales: the mean level spacing delta and the bulk pairing gap Delta(0), which are strongly influenced by the position of the chemical potential with respect to the closest single-electron level. In turn superconducting correlations affect the position of the chemical potential. Within the parity projected BCS model we investigate the probability distribution of the chemical potential in a superconducting grain with randomly distributed single-electron levels. Taking into account statistical fluctuations of the chemical potential due to the pairing interaction, we find that such fluctuations have a significant impact on the critical level spacing delta(c) at which the superconducting correlations cease: the critical ratio delta(c)/Delta(0) at which superconductivity disappears is found to be increased.

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: Recent observation of unusual vortex patterns in MgB2 single crystals raised speculations about possible type-1.5 superconductivity in two-band materials, mixing the properties of both type-I and type-II superconductors. However, the strict application of the standard two-band Ginzburg-Landau (GL) theory results in simply proportional order parameters of the two bandsand does not support the type-1.5 behavior. Here we derive the extended GL formalism (accounting all terms of the next order over the small τ=1-T/Tc parameter) for a two-band clean s-wave superconductor and show that the two condensates generally have different spatial scales, with the difference disappearing only in the limit T→Tc. The extended version of the two-band GL formalism improves the validity of GL theory below Tc and suggests revisiting the earlier calculations based on the standard model.

Abstract: We show that two-band superconductors harbor hidden criticality deep in the superconducting state, stemming from the critical temperature of the weaker band taken as an independent system. For sufficiently small interband coupling gamma the coherence length of the weaker band exhibits a remarkable deviation from the conventional monotonic increase with temperature, namely, a pronounced peak close to the hidden critical point. The magnitude of the peak scales as proportional to gamma(-mu), with the Landau critical exponent mu = 1/3, the same as found for the mean-field critical behavior with respect to the source field in ferromagnets and ferroelectrics. Here reported hidden criticality of multiband superconductors can be experimentally observed by, e.g., imaging of the variations of the vortex core in a broader temperature range. Similar effects are expected for the superconducting multilayers.

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: Recent technological advances resulted in high-quality superconducting metallic nanofilms and nanowires. The physical properties of such nanostructures are governed by the size-quantization of the transverse electron spectrum. This has a substantial impact on the basic superconducting characteristics, e.g., the order parameter, the critical temperature and the critical magnetic field. In the present paper we give an overview of our theoretical results on this subject. Based on a numerical self-consistent solution of the Bogoliubov-de Gennes equations, we investigate how the superconducting properties are modified in the quantum-size regime.