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

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

2009-11-08

arxiv.org/abs/0911.1559v2

Phys. Rev. B 83, 014510 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, 6 figures, journal version

Scientific paper

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.

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