Pairing Fluctuation Theory of Superconducting Properties in Underdoped to Overdoped Cuprates

We propose a theoretical description of the superconducting state of under- to overdoped cuprates, based on the short coherence length of these materials and the associated strong pairing fluctuations. The calculated $T_c$ and the zero temperature excitation gap $\mathrm{\Delta }(0)$, as a function of hole concentration $x$, are in semi-quantitative agreement with experiment. Although the ratio $T_c\mathrm{/}\mathrm{\Delta }(0)$ has a strong $x$ dependence, different from the universal BCS value, and $\mathrm{\Delta }(T)$ deviates significantly from the BCS prediction, we obtain, quite remarkably, quasi-universal behavior, for the normalized superfluid density ${\rho }_s(T)\mathrm{/}{\rho }_s(0)$ and the Josephson critical current $I_c(T)\mathrm{/}{I}_c(0)$, as a function of $T\mathrm{/}{T}_c$. While experiments on ${\rho }_s(T)$ are consistent with these results, future measurements on $I_c(T)$ are needed to test this prediction.