François Peeters

Quantum confinement of electrons in metallic clean nanowires and nanofilms results in the formation of a series of subbands that move in energy with changing thickness. When the bottom of such a subband moves throught the Fermi surface, the density of states changes and a shape resonance appears leading to oscillations in the critical temperature, the critical magnetic field, the critical current and the size of the Cooper pairs as function of the wire/film width. Our theoretical formulation is based on a numerical solution of the Bogoliubov-de Gennes equations. A quantitative description is given of recent experimental data on the thickness dependence of Tc in Al and Sn nanowires and Pb nanofilms.

At a shape resonance the density of the superconducting condensate in a superconducting nanowire is very inhomogeneous, leading to new Andreev-type of states.

In the presence of a parallel magnetic field we predict that the superconductor-to-normal transition at zero temperature occurs as a cascade of subsequent jumps in the order parameter (this is opposed to the smooth second-order phase transition in the mesoscopic regime). Each jump is associated with the depairing of electrons in one of the single-electron subbands. Pronounced quantum-size oscillations of the critical magnetic field with giant resonant enhancements are predicted.

The longitudinal distribution of electrons in a Cooper pair becomes strongly localized when the lower edge of one of the single-electron subbands is close to the Fermi surface. For nanowires made of conventional superconducting materials, the coherence length drops by two-three orders of magnitude and reaches values found in high-Tc superconductors. The underlying physics of this phenomenon suggests it will also be found in other superconducting/superfluid systems with a similar single-fermion spectrum, e.g. in ultrathin metallic nanofilms and atomic Fermi gases confined in a quantum-wire or quantum-well geometry.

In the presence of a parallel magnetic field we predict that the superconductor-to-normal transition at zero temperature occurs as a cascade of subsequent jumps in the order parameter (this is opposed to the smooth second-order phase transition in the mesoscopic regime). Each jump is associated with the depairing of electrons in one of the single-electron subbands. Pronounced quantum-size oscillations of the critical magnetic field with giant resonant enhancements are predicted.