Confinement induced variation of the power-law decay of the order parameter in the low-temperature proximity effect

Abstract

This thesis aims to investigate how the proximity effect is affected by the quantum confinement of charge carriers. This phenomenon, which consists essentially in the diffusion of supercon- ducting correlations into a non-superconducting metal, has been widely studied over several decades, but not so much in the quasi-low dimensionality regime, taking into account the effect of the quantum confinement of electrons on the properties of the system. We aim, more specifically, to determine the functional form for the decay of the pair amplitude in cylindri- cal nanowires of normal metals in the clean limit and at zero temperature. It is known that quantum confinement leads to fluctuations in the values of superconducting quantities, such as the energy gap and transition temperature. This can be expected to affect how strongly the wave function of an electron pair decays in the normal metal. To investigate this problem, we solve the Bogoliubov-de Gennes equations self-consistently in nanowires with different di- ameters. Based on the literature on the proximity effect at low temperatures in clean metals, we model the behavior of the superconducting correlations in the normal metal by an inverse power law decay, with exponent α. The value of this parameter is extracted from the data obtained numerically for each diameter. We found that this parameter follows an oscillatory pattern whose peaks and valleys correspond to those observed in the energy gap.