On Meissner Effect and Superfluid Density in Superconductors

As the most successful microscopic superconductivity theory, Bardeen-Cooper-Schrieffer(BCS) theory has a very peculiar prediction: at zero temperature, only a fraction of electrons within an energy shell form Cooper pair and condense, but all electrons participate to form a macroscopic superfluid and contribute to the superfluid density (inverse square of penetration depth). Very recently, this prediction was challenged by directly measuring the penetration depth upon doping in overdoped cuprates. (Bozovic et al., 2016) Here, we show that such a counter-intuitive prediction of BCS theory is not right. The key point is to disentangle two fundamental concepts in superconductors: plasma frequency and superfluid density, which were thought to be equal for more than half a century. In our theory, superfluid density is determined only by paired electrons while plasma frequency by all electrons. As a consequence, the widely used technique to obtain superfluid density through optical conductivity, based on Ferrell-Glover-Tinkham sum rule, measures only plasma frequency but not superfluid density. Our theory has been evidenced by existed anomalous scaling laws in different experiments.