Disorder Effects on Competition between Antiferromagnetism and Superconductivity in Cuprate Superconductors through the Enhancement in Charge Susceptibility

The coexistence state of antiferromagnetism (AF) and superconductivity (SC) has been observed in five-layered cuprates. However, this coexistence state disappears, and the AF phase and SC phase lose contact in the doping phase diagram toward double- and single-layered cuprates. We investigate the mechanism of the disappearance of the coexistence of AF and SC in disordered cuprate superconductors in order to understand these doping phase diagrams. In single- and double-layered cuprates, electrons on the CuO$_2$ plane experience the disorder effect through inhomogeneity in the charge reservoir layer. These impurity potentials can be effectively enhanced toward the underdoped region by the effect of many-body corrections that involve an increase in charge susceptibility. As a result, strong disorder effects are expected particularly in the competing regions of AF and SC, where the coexistence phase of AF and SC is extremely suppressed. We show the validity of this suppression mechanism by considering the Aslamazov-Larkin-type vertex correction to the effective impurity potential in the effective mean-field phase diagram.