Fixed-N Superconductivity: The Exact Crossover from the Bulk to the Few-Electron Limit

Details Fixed-N Superconductivity: The Exact Crossover from the Bulk to the Few-Electron Limit Fixed-N Superconductivity: The Exact Crossover from the Bulk to the Few-Electron Limit

1999-07-26

arxiv.org/abs/cond-mat/9907402v1

Advances in Solid State Physics, vol. 39, p. 341 (Vieweg Braunschweig/Wiesbaden 1999)

Physics

Condensed Matter

Superconductivity

Short overview (6 pages, 2 figures), comparison to exact results obtained by Richardson in Nuclear Physics

Scientific paper

We use two truly canonical approaches to describe superconductivity in ultrasmall metallic grains: (a) a variational fixed-N projected BCS-like theory and (b) an exact solution of the model Hamiltonian developed by Richardson in context with Nuclear Physics. Thereby we obtain a description of the entire crossover from the bulk BCS regime (mean level spacing $d\ll$ bulk gap $\tilde\Delta$) to the `fluctuation-dominated' few-electron regime ($d\gg\tilde\Delta$). A wave-function analysis shows in detail how the BCS limit is recovered and how for $d\gg\tilde\Delta$ pairing correlations become delocalized in energy space.

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