An Investigation of Electronic Transport Properties for the Cuprates

Abstract

The main purpose of this thesis is to study thermopower measurements of the high temperature superconductors in order to gain insight into the nature of their normal state charge carriers. After noting the previously established pattern for thermopower behaviour, common to all the cuprates, we use phenomenological models to explore possible explanations for this pattern. To begin with, calculations of thermopower are made for the Van Hove scenario. We find that a narrowband singularity by itself cannot produce the cuprate thermopower pattern but if a metallic wideband contribution is included then the cuprate thermopower pattern can be readily produced. Very reasonable fits are obtained to the experimental thermopower data from which we estimate the width of the narrowband singularity to be ~ 0.05 - 0.1 eV, in agreement with various bandstructure calculations. We also uncover deficiencies for a rigid band Van Hove scenario. A pinning mechanism is required to maintain the Fermi level close to the narrowband singularity and there is too much symmetry with respect to varying the hole concentration about optimal doping. Given evidence for localised states to occur in the cuprates, we next investigate the role which localised carriers might play in yielding the cuprate thermopower pattern. We find that a mobility edge picture can explain the cuprate thermopower pattern provided two features are included. The mobility edge must involve a gradual transition, with energy, from a metallic regime to a localised regime whereby metallic and localised carriers co-exist during the transition. Also, the mobility edge must have a temperature dependent energy shift. As to how localised and metallic carriers might co-exist, there is evidence for phase separation to occur in the high-Tc cuprates so we next explore Sheng's theory of fluctuation-induced tunnelling as a possibility for explaining cuprate resistivity and thermopower behaviour. To this end, a major investigation of Sheng's theory is carried out. It is found that Sheng's theory is only valid for 'poor' conductivity systems whereby the conductivity tends exponentially to zero in the zero temperature limit. Hence, we extend the theory to derive a conductivity formula which is also valid for 'good' conductivity systems whereby the conductivity is finite in the zero temperature limit. By deriving an energy dependent conductivity function, we investigate the thermopower behaviour obtained from Sheng's model. We find that if the tunnelling barrier heights are of the order of thermal energies then the cuprate thermopower pattern is readily produced. This model requires that the Fermi level should be pinned and that varying the hole concentration brings about changes in the charge distribution on the Cu-O planes whereby the size of the metallic regions relative to insulating regions is varied. In summary, we find that, while the Van Hove scenario may provide an explanation for the cuprate thermopower pattern, the presence of localised carriers and charge inhomogeneities on the Cu-O planes could also explain this pattern.