Theory of charged impurities in correlated electron materials: Application to muon spectroscopy of high-Tc superconductors

Single-site and cluster dynamical mean-field methods are used to estimate the response of a doped Mott insulator to a charged impurity. The effect of correlations on the Thomas-Fermi screening properties is determined. The charge density, the on-site and near-neighbor spin-spin correlations in the vicinity of the impurity are compared to those far from it. The theory is used to address the question of the effect of the density perturbation induced by the muon charge on the local response functions of a high-temperature superconductor. For reasonable values of the background dielectric constant and basic correlation strength, a muon is shown to lead to an observable perturbation of the local spin dynamics, raising questions about the interpretation of muon-spin-rotation experiments in metallic high-temperature superconductors.