BCS universal ratios in finite systems

Abstract

The BCS universal ratios such as the gap ratio and superconducting jump of the electronic heat capacity normalized to its normal state value are calculated using a simple single-electron model with equal level spacing. The BCS theory predicts that the size dependence of these ratios can be observed in nm-sized clusters if Tc/ωD < 0.1, where ωD is the Debye energy. Under these conditions, the values of these ratios become less than their bulk values in the BCS weak coupling limit. The N-dependence of some analogues of the BCS universal ratios in the canonical formalism is discussed.