Parity effect in mesoscopic and nanoscopic superconducting particles

Superconductivity in small metallic specimens is studied with regard to the size dependence of the parity gap (Delta (P)), a parameter distinguishing between the energy of even and odd number of electrons in the granule. dr is shown to be an increasing function of level spacing delta. The energy gap of superconductor Delta, on the other hand, decreases with increasing delta and vanishes at delta = delta (c) which is of the order of d. However, non-zero value of Delta (P) persists above S, in a gapless superconducting-insulating stale. Level degeneracy in small specimens having perfect geometry changes the size dependence of the parity gap, the Josephson effect, and flux quantization. Parity gap is evaluated using an interpolation procedure between the continuum limit (delta much less than Delta), the moderate mesoscopic regime (delta similar to Delta), and the nanoscopic scale (delta much greater than Delta), for which an exact solution to the pairing problem is provided with the numeric diagonalization of system Hamiltonian in a small metallic cluster. (C) 2001 Elsevier Science B.V. All rights reserved.