Coexistence of the "metallic-like" in-plane and the "semiconducting-like" out-of-plane (caxis) dc conductivities (σ c ), generating a huge anisotropy in the underdoped hightemperature cuprate superconductors (HTCS), defies our current understanding of metal. In this report we present an intrinsic doping dependence of σ c . We find that the σ c for the underdoped HTCS is universally scaled to the σ c at the optimal doped-hole concentration.The universal scaling behavior suggests that there are three intrinsic processes contribute to σ c : (i) the doping-dependent-activated gap; (ii) the exponential doping dependences and (iii) the tunneling between adjacent CuO 2 block layers. They are the essential underlying characteristics of the c-axis transport for all HTCSs.
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IntroductionPlanar doped-hole concentration (P pl ) is one of the most important physical parameters that dictate both normal and superconducting properties of high-temperature cuprate superconductors (HTCS). In order to systematically compare the doping dependence of various in-plane properties among different HTCSs, we have constructed the hole-scale based on the universal relation between the in-plane thermoelectric power at 290 K (S 290 ) and P pl [1]. The hole-scale is derived from, therefore consistent with, the relation between S 290 and P pl of single-layer La 2-x Sr x CuO 4 (P pl = x) and double-layer Y 1-x Ca x Ba 2 Cu 3 O 6 (P pl = x/2). Until now, although there have been many temperature (T)-dependent studies of c-axis dc conductivity (σ c ) , there are few qualitatively doping-dependent studies of σ c for many different HTCSs [39,40]. In the T-dependent studies one has to deal with many Tdependent factors involving possible changes of electronic band structure, of scattering rate and structural phase transitions. On the other hand, the doping-dependent studies have the distinct advantages of directly studying the evolution of the electronic states upon holedoping without the complications due to the variation of T. Doping induced properties that are generic to all materials will be the real intrinsic properties of HTCS which warrant serious considerations.In this paper, we have analyzed σ c of 19 hole-doped HTCSs from 37 published papers . We found that the doping dependence of σ c for HTCSs is well scaled by P pl opt ,where the HTCS material has the highest T c , and σ c opt , which is the conductivity at P pl opt .The universal scaling behavior suggests that the intrinsic contributions of the dopingdependent-activated gap, the exponential doping dependences and the tunneling between adjacent CuO 2 block layers are essential and underlying the c-axis transport for all HTCSs.
Analysis methodBased on the hole-scale proposed in [1], we use two methods to extract the doped-hole concentration from the published data: P pl is determined from the value of S 290 by using the formula reported in [1] and, as the first and preferred method, P pl so determined is most reliable. Using first method we fou...