BCS superconductivity in metallic nanograins: Finite-size corrections, low energy excitations, and robustness of shell effects

Abstract

We combine the BCS self-consistency condition, a semiclassical expansion for the spectral density and interaction matrix elements to describe analytically how the superconducting gap depends on the size and shape of a 2d and 3d superconducting grain. In chaotic grains mesoscopic fluctuations of the matrix elements lead to a smooth dependence of the order parameter on the excitation energy. In the integrable case we find shell effects i. e. for certain values of the electron number $N$ a small change in N leads to large changes in the energy gap. With regard to possible experimental tests we provide a detailed analysis of the dependence of the gap on the coherence length and the robustness of shell effects under small geometrical deformations.

16 pages, 6 figures, journal version

References in corpus (5)

• Inhomogeneous superconductivity and the "pseudogap state of novel superconductors
• Shell Structure and Strengthening of Superconducting Pair Correlation in Nanoclusters
• Upper critical field in nanostructured Nb: Competing effects of the reduction in density of states and the mean free path
• Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory
• Critical temperature and specific heat for Cooper pairing on a spherical surface

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