Gap spectroscopy in underdoped YBa$_2$Cu$_3$O$_{6+x}$ from superfluid spectral weight and intrinsic pair tunneling

Numerous experiments on cuprate high temperature superconductors reveal evidence for two different energy gaps: a normal state pseudogap that grows on underdoping, and a superconducting gap connected to the transition temperature $T_c$ [1]. Here we use two different experiments to probe the superconducting energy gap scale in highly underdoped YBa$_2$Cu$_3$O$_{6+x}$: intrinsic pair tunneling perpendicular to the CuO$_2$ planes; and measurements of in-plane superfluid spectral weight. The measurements have been carried out on special samples in which doping can be tuned continuously using controlled oxygen annealing at room temperature [2]. We present data for $T_c$ in the range of 3~K to 17~K, and show that the superconducting energy gap is indeed linked to $T_c$ (2$\Delta \sim 4 k_B T_c$), vanishing as $T_c \rightarrow 0$. \\[4pt] [1] H\"{u}fner \emph{et al.} Rep. Prog. Phys. 71, 062501 (2008)\\[0pt] [2] Broun \emph{et al.} Phys. Rev. Lett. 99, 237003 (2007)