Fractal nature and scaling exponents of non-Drude currents in non-Fermi liquids

Abstract

In many oxides of the perovskite and pseudoperovskite families there are phase transitions between insulating and normal metallic (Fermi-liquid) phases that are separated by an intermediate phase that is often called a non-Fermi liquid. The dc resistivity of the intermediate or non-Fermi-liquid phase often exhibits a T temperature dependence, in contrast with the T² dependence expected from a bad normal metal. The same alloys exhibit a non-Drude w^2a frequency dependence, with α ≈ 0.5, in contrast with the Drude dependence w² characteristic of samples with the T² behaviour. Various attempts have been made to modify the algebra of continuum Fermi-liquid theory to derive the non-Drude exponent α, but these have been based on artifices designed to explain only this one parameter. The discrete filamentary model has been used to calculate many properties of high-temperature superconductors, and to explain the asymmetric nature of the intermediate phase. Here it is used to derive N by the same rules previously used for several other discrete relaxation calculations that are in excellent agreement with other quite different experiments. The results are, for (cubic) perovskites, α = 0.45 and, for planar conductivity of bilayered pseudoperovskites, α = 0.70. The corresponding experimental values are (0.4, 0.5) and 0.7.