  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.
