Temperature and magnetic field dependence of superconductivity in nanoscopic metallic grains

We study pairing correlations in ultrasmall superconductor in the nanoscopic limit by means of a toy model where electrons are confined in a single, multiply degenerate energy level. We solve the model exactly to investigate the temperature and magnetic field dependence of number parity effect (dependence of ground state energy on evenness or oddness of the number of electrons). We find a different parity effect parameter to critical temperature ratio (=~ 4 rather than 3.5) which turns out to be consistent with exact solution of the BCS gap equation for our model. This suggest the equivalence between the parity effect parameter and the superconducting gap. We also find that magnetic field is suppressed as temperature increases.