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.
