Thermodynamics and Critical Current Density in High- $T_{\mathrm c}$ Superconductors

The relationships between the superfluid density on the one hand and critical current density, pinning, irreversibility field, condensation energy and fluctuations, on the other, are explicitly derived. These are established by standard thermodynamic relationships and are quantified by direct measurements of the electronic specific heat and superfluid density. As we show, each of these properties is dependent only on the superfluid density, defined as the inverse square of the London penetration depth. In the case of the high-T_c cuprates the superfluid density is strongly suppressed due to the presence of the competing pseudogap, even at optimal doping where T_c maximizes. The pseudogap thus plays a pathological role in limiting the critical current and to optimize this a sample must be overdoped precisely to the critical doping point (p ≈ 0.19 holes/Cu) where the pseudogap closes.