Universal scaling of the cc-axis dc conductivity for underdoped high-temperature cuprate superconductors

The coexistence of ‘metallic-like’ in-plane dc conductivity and ‘semiconducting-like’ out-of-plane   (cc-axis) dc conductivity (σc)(σc), generating huge anisotropy in underdoped high-temperature cuprate superconductors (HTCSs), defies our current understanding of metals. In this report, we present an intrinsic doping dependence of σcσc. We find that σcσc for underdoped HTCSs is universally scaled to the σcσc value at the optimal doped-hole concentration. The universal scaling behavior suggests that there are three intrinsic processes that contribute to σcσc: (i) the doping-dependent-activated gap; (ii) the exponential doping dependences, and (iii) the tunneling between adjacent CuO2 block layers. They are the essential underlying characteristics of the cc-axis transport for all HTCSs.