Search for Cooper-pair Fluctuations in Severely Underdoped YBCO Films

The preformed-pairs theory of pseudogap physics in high-$T_C$ superconductors predicts a nonanalytic $T$-dependence for the $ab$-plane superfluid fraction, ${\rho }_S$, at low temperatures in underdoped cuprates. We report high-precision measurements of ${\rho }_S(T)$ on severely underdoped YBa${}_2$Cu${}_3$O${}_{6+x}$ and Y${}_{0.8}$Ca${}_{0.2}$Ba${}_2$Cu${}_3$O${}_{6+x}$ films. At low $T$, ${\rho }_S$ looks more like $1-T^2$ than $1-T^{3\mathrm{/}2}$, in disagreement with theory.