Impurities and Defects in Mott Systems

Disorder has intriguing consequences for correlated electronic materials, which include several families of high-temperature superconductors and resistive switching systems. In this dissertation, we study the effects of impurities intertwined with correlations. First, we study impurity healing effects in models of strongly correlated superconductors. We show that in general both the range and the amplitude of the spatial variations caused by nonmagnetic impurities are significantly suppressed in the superconducting as well as in the normal states. We explicitly quantify the weights of the local and the non-local responses to inhomogeneities and show that the former are overwhelmingly dominant over the latter. We find that the local response is characterized by a well-defined healing length scale, which is restricted to only a few lattice spacings over a significant range of dopings in the vicinity of the Mott insulating state. We demonstrate that this healing effect is ultimately due to the suppression of charge fluctuations induced by Mottness. We also define and solve analytically a simplified yet accurate model of healing, within which we obtain simple expressions for quantities of direct experimental relevance. Second, we address the question of why strongly correlated d-wave superconductors, such as the cuprates, prove to be surprisingly robust against the introduction of non-magnetic impurities. We show that, very generally, both the pair-breaking and the normal state transport scattering rates are significantly suppressed by strong correlations effects arising in the proximity to a Mott insulating state. We also show that the correlation-renormalized scattering amplitude is generically enhanced in the forward direction, an effect which was previously often ascribed to the specific scattering by charged impurities outside the copper-oxide planes. Finally, we provide the theoretical insights for resistive switching systems and show how impurities and underlying correlations can play significant roles in practical devices. We report the striking result of a connection between the resistive switching and shock wave formation, a classic topic of non-linear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide based memristor device and we extend our theory to the case of binary oxides. The shock wave scenario brings unprecedented physical insight and enables to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect – the commutation speed.