Dependence of superconducting properties on the size and shape of a nanoscale superconductor: From nanowire to film

We analyze the dependence of the basic superconducting quantities-the order parameter, energy gap, and critical temperature-on the size and shape of a nanoscale superconductor in the clean limit. The Bogoliubov-de Gennes equations are solved numerically for a metallic nanowire with rectangular cross section. This makes it possible to vary the confining geometry, passing from a nanowire to a nanofilm and testing the sensitivity of the basic superconductive characteristics on the transverse size and shape of the nanowire. Strong size and shape superconducting resonances are found that depend on the geometry of the sample.