Transição metal-isolante induzida por desordem e interação elétron-elétron. - Whittemberg da Silva Oliveira (2010)
A metal-insulator transition takes place in systems for which the electron-electron interaction energy gets comparable or larger than the kinetic energy. In the absence of chemical impurities (disorder), this corresponds to the Mott transition, which can be described by thecharge transfer model. This consists of a two band model: one band correspond to conduction electrons and the other to localized or f -electrons. The former is large, which makes the electron-electron relatively negligible, while the latter is narrow, meaning that electron- electron interaction is relatively strong. In the charge transfer model, the sum, per site, of the occupation number for conduction electrons and the occupation number for f -electrons is equal to one. The proximity to the insulating phase is obtained when the f -electron energy, Ef decreases,implying in the transfer of charge to the f -electron states and in the decrease of the occupation for conduction electrons. The Mott transition occurs when the number of conduction electrons per site becomes zero.In the case of disordered non-interacting systems, a metal-insulator transition can also occur, due to disorder, which produces Anderson localization effects. Our interest is to study correlated disordered systems, where an interplay between electron-electron interaction and disorder effects drive can systems through a metal-insulator transition. Moreover, in the metallic phase of these systems, an electronic Griffiths phase with non-Fermi liquid behavior is observed. This non-Fermi liquid behavior appears for values of disorder smaller than that where thetransition happens, and corresponds to the emergence of the Griffiths phase. In this phase two types of spins exist, those which behave as free spins and those that form a singlet state with conductions electrons. The former dominate the thermodynamic response of the system, givingrise to non-Fermi liquid behavior. In this work, we use a combination of dynamical mean field theory and typical-medium theory to solve the disordered charge transfer model and to study the emergence of the Griffiths phase and the metal-insulator transition. Disorder is considered in the on-site energy for conduction electrons, wich follows a gaussian distribution of standard deviation W. We analyze both the results obtained for different values of Ef , when disorder is kept constant, as well as the results obtained for different values of disorder, when Ef is kept constant. In both cases the method is able to describe the metal-insulator transition and the Griffiths phase. When Ef /D = -1.3 (where D is the conduction electron bandwidth in the clear case), the Griffiths phase appears for disorder W/D & 0.3 but ceases to exist long before the transition, which happens for disorder W/D 6.1. For fixed disorder, W/D = 1.5, the Griffiths phase emerges for Ef /D -1.3 and persists up to the transition, which occurs for Ef /D -3.1. All results were obtained at zero temperature.