Low Temperature Superfluid Response of High-T_c Superconductors

We have reviewed our theoretical and experimental results of the low temperature superfluid response function of high temperature superconductors (HTSC). In clean high-T_c materials the in-plane superfluid density varies linearly with temperature. The slope of this linear T term is found to scale approximately with 1/T_c which, according to the weak coupling BCS theory for a d-wave superconductor, implies that the gap amplitude scales approximately with T_c. A T⁵ behavior of the out-of-plane superfluid density for clean tetragonal HTSC was predicted and observed experimentally in the single layer Hg-compound HgBa₂CuO_4+δ. In other tetragonal high-T_c compounds with relatively high anisotropy, such as Hg₂Ba₂Ca₂Cu₃O_8+δ, varies as T² due to disorder effects. In optimally doped YBa₂Cu₃O_7-δ, varies linearly with temperature at low temperatures, but in underdoped YBa₂Cu₃O_7-δ, varies as T² at low temperatures; these results are consistent with our theoretical calculations.