Nanoscale superconductivity: Nanowires and nanofilms

Quantum confinement of electrons in highly crystalline nanowires and nanofilms results in the formation of a series of subbands that move in energy with changing wire/film thickness. When the bottom of such a subband moves through the Fermi surface, the density of states changes and a size-dependent superconducting resonance appears, leading to quantum-size oscillations in the critical temperature TcTc (the order parameter and energy gap) and the critical magnetic field HcHc as function of the thickness. Our theoretical formulation is based on a numerical solution of the Bogoliubov–de Gennes equations in the clean limit. A quantitative description is given of recent experimental data on the thickness dependence of TcTc in Al and Sn nanowires, and on the film thickness dependence of TcTc in Al and Pb nanofilms. In the presence of quantum confinement the spatial distribution of the pair condensate is very inhomogeneous, which leads to the formation of new Andreev-type states induced by quantum confinement. Our investigation suggests that these states can play an important role in superconducting nanowires, decreasing the ratio of the energy gap to the critical temperature. We also show that for cylindrical nanowires with diameters ≲10–15nm, the superconducting-to-normal phase transition driven by a parallel magnetic field becomes of first order. The critical field is strongly enhanced, and exhibits pronounced quantum-size oscillations.