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

The coexistence of ‘metallic-like’ in-plane dc conductivity and ‘semiconducting-like’ out-of-plane ( c -axis) dc conductivity ( σ c ) , 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 σ c . We find that σ c for underdoped HTCSs is universally scaled to the σ c value at the optimal doped-hole concentration. The universal scaling behavior suggests that there are three intrinsic processes that contribute to σ c : (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 c -axis transport for all HTCSs.