Low Temperature Superfluid Response of High-tc Superconductors

We have reviewed our theoretical and experimental results of the low temperature superfluid response function ρs of high temperature superconductors (HTSC). In clean high-Tc materials the in-plane superfluid density ρ ab s varies linearly with temperature. The slope of this linear T term is found to scale approximately with 1/Tc which, according to the weak coupling BCS theory for a d-wave superconductor, implies that the gap amplitude scales approximately with Tc. A T 5 behavior of the out-of-plane superfluid density ρs for clean tetragonal HTSC was predicted and observed experimentally in the single layer Hg-compound HgBa2CuO4+δ. In other tetragonal high-Tc compounds with relatively high anisotropy, such as Hg2Ba2Ca2Cu3O8+δ, ρ c s varies as T 2 due to disorder effects. In optimally doped YBa2Cu3O7−δ, ρ c s varies linearly with temperature at low temperatures, but in underdoped YBa2Cu3O7−δ , ρ c s varies as T 2 at low temperatures; these results are consistent with our theoretical calculations.