What Were Solved and What Should Be Solved in Heavy Fermion Systems

Abstract

Present theoretical status to understand various anomalous properties of valence fluctua­ tion and heavy fermion systems is reviewed and some new models are proposed. Mostly Ce-compounds are treated. At first the fundamental Hamiltonian is considered quantitatively. Some effective Hamiltonians are deduced from it and their validities are checked. Then it is shown that the /-band model serves a good starting point for the valence fluctuation regime while the split /-band model is suitable for the Kondo regime. Approach from the impurity Kondo state is reviewed briefly. Nesting of a small part of Fermi surface and different types of pairing in the Fermi surfaces with different characters are proposed for mechanisms of various heavy fermion superconductivities. It is shown that magnetic polarons and magnetic polaron crystalization are important in the very low carrier heavy fermion systems such as Sm3Se4, Gd2S3 and CeSb.