Thesis presented October 29, 2004

Abstract:
he first part of the thesis is devoted to the study of the fixed points associated with a generalized Kondo model. This work is motivated by the recent discovery of a non Fermi liquid behavior in some heavy fermion compounds. We consider a single impurity Kondo model, with an impurity spin described by a mixed representation of the SU(N) group, combining both bosonic and fermionic degrees of freedom. The stability of the strong coupling fixed point is discussed within a second order perturbation theory around this fixed point. Contrarily to the Kondo models studied so far, we find an instability of the strong coupling fixed point for a certain class of representations of the impurity spin already in the case of a single channel for conduction electrons. This instability indicates that the physics of the system is described by an intermediate coupling fixed point, generally characterized by a non Fermi liquid behavior. We develop an approach based on the perturbative renormalization group, in order to identify this intermediate coupling fixed point. We derive the ß scaling function characterizing the renormalization flow and derive the low energy properties of the system.
In a second part, we study the high temperature superconductivity of hole doped cuprates on the basis of a magnetic-type interpretation. The origin of the superconducting instability is attributed to the coexistence of two mechanisms. The first mechanism that is considered corresponds to the formation of a spin density wave, resulting from the exchange of antiferromagnetic spin fluctuations in an almost antiferromagnetic state, as it is proposed in the "spin bag" theory. The second one supposes the existence of a resonating valence bond state (RVB), with the formation of a spin singlet in the Copper-Oxygen plans. Both mechanisms predict the appearance of a superconducting phase away from the half filling. We develop a mean field theory, which allows to describe the coexistence of both mechanisms. Using a functional integration formalism, we derive the effective BCS-type pairing interaction among quasiparticles, mediated by the gaussian fluctuations (at a RPA level) of the different considered fields. The symmetry of the superconducting gap is also discussed.

Keywords:
Condensed matter theory, strongly correlated electronic systems, Kondo effect, High-temperature supreconductivity

On-line thesis.