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

Fabian Braun; Jan von Delft

doi:10.1103/physrevlett.81.4712

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

Fabian Braun·Jan von Delft

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Abstract

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 $\tildeΔ$) to the ``fluctuation-dominated'' few-electron regime ($d\gg\tildeΔ$). A wave-function analysis shows in detail how the BCS limit is recovered for $d\ll \tilde Δ$, and how for $d \gg \tilde Δ$ 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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Fabian Braun, Jan von Delft. 1999-01-18. Fixed-N Superconductivity: The Crossover from the Bulk to the Few-Electron Limit. https://doi.org/10.1103/physrevlett.81.4712

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