Abstract: The BCS coherence length in low-dimensional superconductors is dramatically modified by quantum-size effects. In particular, for nanowires made of conventional superconducting materials, we show that the longitudinal zero-temperature coherence length exhibits width-dependent drops by 23 orders of magnitude each time when the bottom of one of single-electron subbands formed due to the transverse quantization of electron motion is situated in a close vicinity to the Fermi level. This phenomenon has strong similarities to the well-known BCS-BEC (Bose-Einstein condensation) crossover in ultracold fermionic condensates but with an important exception: it is driven by the transverse quantization of the electron motion rather than by the externally controlled strength of the fermion-fermion interaction.

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: We propose an improved image simulation procedure for atomic-resolution annular dark-field scanning transmission electron microscopy (STEM) based on the multislice formulation, which takes thermal diffuse scattering fully into account. The improvement with regard to the classical frozen phonon approach is realized by separating the lattice configuration statistics from the dynamical scattering so as to avoid repetitive calculations. As an example, the influence of phonon scattering on the image contrast is calculated and investigated. STEM image simulation of crystals can be applied with reasonable computing times to problems involving a large number of atoms and thick or large supercells.

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: We demonstrate that in quantum-dot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both dephasing mechanisms strongly affects the transition from the weak-to the strong-coupling regime as well as the shape of the spectral triplet that represents the quantum-dot occupation in Fourier space. The width of the central peak in the triplet is expected to decrease with rising temperature, while the widths and heights of the side peaks depend nonmonotonically on the dot-cavity coupling.

Abstract: In 1956 Cooper demonstrated (1956 Phys. Rev. 104 1189) that, no matter how weak the attraction is, two electrons in three-dimensional (3D) space just above the Fermi sea could be bound. In this work we investigate the influence of confinement on the binding energy of a Cooper pair. We show that confinement-induced modification of the Fermi sea results in a significant increase of the binding energy, when the bottom of an energy subband is very close to the Fermi surface.

Abstract: Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. In addition, there is experimental evidence that whether an enhancement or a reduction is found depends on the strength of the electronphonon interaction in the bulk. We reveal how the strength of the e-ph interaction interplays with the quantum-size effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data. We demonstrate that strong e-ph scattering smears the peak structure in the electronic density-of-states of a metallic grain and enhances the electron mass, and thereby limits the highest T-c achievable by quantum confinement.