Localização de Anderson e transição metal-isolante em sistemas fortemente interagentes com dopagem

Abstract

In this thesis we study strongly correlated electrons systems in the presence of disorder and doping. The correlations treated here, denoted by U, are between electrons that repel each other when they are at the same site. Disorder W causes variations in the onsite energy levels sites with different energies have the same probability of occurring in the lattice. Doping delta causes the system to have different electronic occupancies. It can be changed by controlling the chemical potential. In this work we analyze what occurs when U, W and delta act simultaneously in a physical system, which originates a plurality of phenomena. The motivation for our study comes from different experimental results, and no specific material is analyzed. It is known that materials such as rare earths, actinides, transition metals and their oxides have strong local electronic interaction. To study these materials it can be useful to add doping, which inevitably can cause disorder effects in the material. These systems can be found in different phases such as Fermi liquid, Mott insulator, Anderson insulator, or a phase generated by a combination of phenomena, which motivates us to make a description of how each parameter (U, W and delta) can be combined with each other. To consider both the local correlation U and the disorder W, we work with the Anderson-Hubbard model, which takes into account the kinetic energy of electrons, the Coulomb interaction and the disorder in the onsite energy. The methodology we use to solve the Anderson-Hubbard model is the Dynamical Mean Field Theory, used to treat interacting systems, combined with the Typical Medium Theory, used to treat disorder. Our results are summarized in the phase diagrams of W versus delta for different values of U, built from numerically and analytically calculated data. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites. Thus, our work has contributed to a better understanding of disorder and doping effects in strongly correlated systems.