Efeitos de localização de Anderson próximo à transição metal-isolante de Mott - Helena de Souza Braganca (2014)
The Coulomb repulsion between electrons strongly a ects the properties of a class of materials, which can go through a metal-insulator phase transition - the so called Mott transition, when this interaction energy becomes more relevant than the system kinetic energy. The presence of disorder also limits the electron mobility and can drive the systems through the Anderson metalinsulator transition. These two mechanisms for localization combine themselves, sometimes enhancing, sometimes reducing the e ects of each other. This interplay is important in real systems and is observed in experimental works performed on compounds such as transition metal oxides and organic salts, which show strong Coulomb repulsion. Experimentally, doping can be added to these systems with the goal of introducing chemical pressure, thus reducing the ratio between electron-electron interaction and kinetic energies; this procedure, however, adds disorder to the systems. Considerable progress on the description of Mott and Anderson transitions has been achieved in the last few decades due to the development of numerical approaches that are able to describe correlated and disordered systems. The transition driven by interactions can be described by dynamical mean eld theory, while typical medium theory provides a description of localization due to disorder. The combined e ect of both interactions and disorder on the electronic wave functions, specially on their possible localization, is not well established in the literature, however, and is the subject of this work. We use a combination of dynamical mean eld theory and typical medium theory to study the Hubbard model, which describes the competition cited above between electron-electron interaction and kinetic energies. In our model, the electron local energy changes from site to site according to a disorder distribution. Our calculation is performed at nite temperature. We are able to analyze di erent regions of the phase diagram valid for correlated systems in the presence of disorder. Below a critical temperature Tc, the Mott transition is of rst order and a metal-insulator coexistence region exists. According to our results, Anderson localization has important e ects near the Mott transition, specially on the coexistence region, even in the limit of small to moderate disorder. In particular, we observe that Anderson localization e ects decrease the critical interaction at which Mott transition occurs, as well as produce a narrower coexistence region in comparison with results obtained via standard-DMFT, which does not include Anderson localization e ects. In addition, we analyze how disorder a ects Tc. Our numerical data suggest that the critical temperature of the Mott transition goes to zero as we increase disorder, revealing the quantum critical point of this transition, which, for smaller disorder, is \hidden" by the coexistence region. Our results in other regimes of the phase diagram con rm conclusions known in the literature. In the limit of small U, near the Anderson transition, for example, we observe an e ect of disorder screening due to interactions. Furthermore, we see that both Anderson and Mott routes to localization are relevant in the regime of strong, comparable values of interaction and disorder. In this case, we describe a direct crossover between Mott and Anderson insulators, with the absence of an intermediate metallic phase.