Resistivity and Hall effect of metallic oxygen-deficient YBa₂Cu₃O_x films in the normal state

We present a systematic study of normal-state transport properties in a series of c-axis-oriented YBa₂Cu₃O_x (YBCO) epitaxial thin films and YBa₂Cu₃O₇/PrBa₂Cu₃O₇ (YBCO/PrBCO) superlattices. The hole doping level in the YBCO films is varied from the optimum-doped metallic down to the underdoped insulating regime by changes in the oxygen content x. We find that the magnitude of the resistivity ρ and Hall coefficient R_H increases monotonically with decreasing x and that their respective temperature dependences undergo marked changes. The R_H(T) behavior is reminescent of the Hall effect behavior in heavy fermion metals, taking into account a difference in temperature by a factor of 100. The Hall angle cotθ_H=ρ/R_HB shows a quadraticlike temperature dependence, with systematic deviations at high and low doping levels. Transport measurements in YBCO/PrBCO superlattices, with the YBCO layers in the two-dimensional regime, indicate that the deviations of a T² dependence of the Hall angle are intrinsic and not related to the dimensionality of the system. A method of analyzing the transport data is presented, revealing a striking scaling behavior of the respective properties. A comparison with reported transport data in the literature suggests that the observed scaling behavior may be universal for underdoped cuprates. Furthermore, we show that reported NMR Knight shift data for oxygen-deficient YBCO samples can also be mapped on a single scaling curve, by using the same scaling parameter derived from our transport measurements. This finding strongly indicates that the dominant scattering mechanism in these materials is of magnetic origin. Going one step further, we present a qualitative analysis of the conductivity under the assumption that we may use the expression for a two-dimensional quantum liquid and that the inelastic scattering length may be replaced by the magnetic correlation length ξ(T). Expressions for the latter are taken from reported calculations for undoped and doped cuprates. A good qualitative agreement is obtained between the calculated and experimentally observed temperature-dependent conductivity.