Fixed-N superconductivity: The crossover from the bulk to the few-electron limit

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 much less than bulk gap <(Delta)over tilde>) to the "fluctuation-dominated" few-electron regime (d much greater than <(Delta)over tilde>). A wave-function analysis shows in detail how the BCS limit is recovered for d much less than <(Delta)over tilde>, and how for d much greater than <(Delta)over tilde> pairing correlations become delocalized in energy space. An earlier grand-canonical prediction fur an observable parity effect in the spectral gaps is found to survive the fixed-N projection. [S0031-9007(98)07675-3].