Valence fluctuations and disorder effects in strongly correlated electronic systems

Abstract

In this thesis, we have carried out theoretical investigations of valence fluctuations and disorder effects in strongly correlated electron systems, focusing on heavy fermion materials in particular. The theoretical framework that we have employed is that of dynamical mean field theory (DMFT), which allows the mapping of a lattice model to a self-consistently determined effective impurity problem. We have extended, implemented and applied the semi-analytical, local moment approach to solve the impurity model. The first three chapters have a common theme – namely valence fluctuations driven crossovers and transitions. The periodic Anderson model, a paradigm to understand heavy fermions in rare-earth systems, has been employed in the first chapter to study a valence crossover, and the manifestation of this crossover in optical and transport properties. A detailed comparison to DC and optical transport of several Cerium and Ytterbium based materials yields excellent agreement. The valence crossover investigated in the first chapter can be transformed to valence transitions with an additional term, i.e inter-orbital Coulomb interaction term in the PAM Hamiltonian, leading to an extended periodic Anderson model, that is investigated in chapter two. A valence fluctuations driven quantum critical point is found to exist in realistic parameter regimes. In order to access real systems, one must be able to deal with orbital degeneracy and interorbital correlations.