Pair-mixing superconducting correlation in ultrasmall metallic grains - art. no. 054511

The superconducting order in an ultrasmall metallic grain with a fixed numb er of electrons is analyzed. By exploiting the intrinsic symmetries of the BCS Hamiltonian, we establish some general properties of a recently propose d pair-mixing correlation function on a mathematically rigorous basis. We a lso prove a relation between this function and the conventional off-diagona l correlation function. By variationally estimating both correlation functi ons, we show that the superconducting crossover in ultrasmall metallic grai ns is smooth, a conclusion reached previously by numerical calculations.