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

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

1998-10-13

arxiv.org/abs/cond-mat/9810146v2

Phys. Rev. Lett. 81, 4712 (1998)

Physics

Condensed Matter

Superconductivity

4 pages, 3 figures, RevTeX, V2: minor charges to mach final printed version

Scientific paper

10.1103/PhysRevLett.81.4712

We present a truly canonical theory of superconductivity in ultrasmall metallic grains by variationally optimizing fixed-N projected BCS wave-functions, which yields the first full 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 for $d\ll \tilde \Delta$, and how for $d \gg \tilde \Delta$ pairing correlations become delocalized in energy space. An earlier grand-canonical prediction for an observable parity effect in the spectral gaps is found to survive the fixed-N projection.

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