The study of some physical properties of high temperature superconductors

The phenomenon of superconductivity, the discovery of high temperature superconductivity in the Cuprates and the properties of these materials is described in the introductory chapter. It also includes a discussion of the pseudogap, which has remained a mystery as has the high transition temperature. Possible applications of high temperature superconductivity are reviewed before the theories by Bardeen, Cooper, and Schrieffer (BCS) and Ginzburg and Landau are briefly sketched. The last section gives excerpts of the by now vast literature on this subject, focussing on the role impurities play in this context. The second chapter develops the mathematical tools and the theoretical background for the description of many-body systems. Various Green's functions are introduced which are then used to describe scattering of quasiparticles off defects of arbitrary strength. They are also required to calculate the a.c. conductivity, for which an expression is derived using linear response theory. The convergence problems one encounters when actually calculating the conductivity are briefly discussed. Detailed calculations for the normal state are presented in the third chapter and in the appendix. The third Chapter begins with a detailed presentation of the tight binding model for the energy dispersion because this model appears to give a more accurate description of the electronic properties of high temperature superconductors than the nearly free electron model. The shape of the two-dimensional Fermi surface is calculated and displayed as function of band filling and the next-nearest neighbor hopping integral B, assuming a rigid band. B plays an important role in the formation of so-called hot spots. The quasiparticle density of states and its Hilbert transform F(ω) are solved by means of complete elliptic integrals formalism. These results are used to obtain impurity bound states. A simple model for the superconductivity in the cuprate materials is developed on the basis of hot spots and the pseudogap, particularly relevant for the electron doped materials, where electrons and holes might coexist, depending on the degree of doping. (orig.)