Thesis presented October 23, 2001

Abstract:
This thesis revolves around a main subject: the theoretical study of the Kondo effect in heavy fermions when the magnetic impurity concentration is high.
In the first part, the influence of the variation of the concentration of conducting electrons on the Kondo lattice is studied at low temperature (exhaustion problem).
This effect can be observed experimentaly in some Cerium and Uranium compounds, whose coherence temperature can be considerably small compared to the predictions of single impurity models. The study is made both analyticaly and numericaly in the "large-N" limit, where N is the number of spin components. Whereas the single impurity models are caracterised at low temperature by a single energy scale, T_K this thesis confirms the existence for the Kondo lattice of a second scale T*, caracterising the appearance of the Fermi liquid behavior.
In the second part, the effects of disorder and magnetic frustration are studied analyticaly, within the dynamical mean field theory formalism, in the "large-N" limit. A quantum critical point (QCP) is obtained between a heavy Fermi liquid regime and a spin liquid regime. The physical properties of the system are computed in the Kondo phase. In particular, a strong decrease of T* and d is obtained in the vicinity of the QCP. This result is correlated with the large effective mass that has been experimentaly mesured for the compound LiV₂O₄.
Finaly, the third part presents a preliminary study and the outline of the computation procedure leading to the numerical determination of the magnetic phase diagram of the periodic Anderson Model, using the dynamical mean field theory method.

Keywords:
Kondo lattice, spin liquid, Fermi liquid, disorder, frustration, heavy fermions, quantum critical points

On-line thesis. ​