Theoretical studies of phase transitions and transport properties in high-temperature superconductors and quasi-one-dimensional organic metals

The problem of the ground states of the high-{dollar}Tsb{lcub}c{rcub}{dollar} superconductors is approached by considering the electron system with flat regions on the opposite sides of the Fermi surface. The possible instabilities are classified in the framework of the parquet approximation and corresponding renormalization-group equations, that determine the evolution of susceptibilities with decreasing temperature, are solved numerically. Solutions of the parquet equations are found to be in qualitative agreement with a ladder approximation. For the repulsive Hubbard interaction, the antiferromagnetic (spin-density-wave) instability dominates, but when the Fermi surface is not perfectly flat, the d-wave superconducting instability takes over.; The phenomenology of the high-{dollar}Tsb{lcub}c{rcub}{dollar} superconductors is studied on the basis of ac and dc magnetotransport data in the normal state of {dollar}rm YBasb2Cusb3Osb7{dollar} within the Fermi-liquid and non-Fermi-liquid models. In the Fermi-liquid analysis we use the Fermi surface deduced from the band structure calculations and assume that the electron relaxation rate varies over the Fermi surface. Introducing two characteristic scattering times, an additive two-{dollar}tau{dollar} model is formulated, and corresponding phenomenological parameters are determined. The non-Fermi-liquid models are the two-dimensional Luttinger liquid model and the charge-conjugation-symmetry model. The existing experimental data can be adequately fitted by any of these models, not allowing to discriminate among these concepts.; The second part of the dissertation is devoted to the umklapp resistivity of the quasi-one-dimensional organic conductors in the magnetic field. The magnetoresistance in the classical magnetic field is considered due to the nonhomogeneous distribution of the electron scattering rate on the Fermi surface. Microscopical calculations show that in certain regions on the Fermi surface the scattering rate is indeed anomalously high. The reason for the existence of these "hot spots" is analogous to the appearance of the van Hove singularities in the density of states. In a generalized {dollar}tau{dollar}-approximation, where the scattering integral in the Boltzmann equation is replaced by the scattering time which depends on the position at the Fermi surface, the resistivity is studied as a function of the amplitude and the orientation of the magnetic field.; In the quantized magnetic field the umklapp resistivity is derived on the basis of the variational principle for the Boltzmann kinetic equation, where the antiferromagnetic fluctuations are taken into account in the framework of the mean-field formalism. Numerical calculations show the significant effect of the phase defined by the electron dispersion: the strong magnetoresistance for {dollar}varphisb{lcub}b{rcub}=0{dollar} at temperatures above transition temperature, and no magnetoresistance at the generic phase. The {dollar}varphisb{lcub}b{rcub}=0{dollar} results, however, do not provide the adequate experimental temperature dependence of resistivity in the zero magnetic field.