Two-Dimensional Nature of Four-Layer Superconductors by Inequivalent Hole Distribution

The magnetization of the four-layer superconductor CuBa_{2}Ca_{3}Cu_4O_{12-\delta} with T_c\simeq117 K is presented. The high-field magnetization around T_c(H) follows the exact two-dimensional scaling function given by Te\v{s}anovi\'{c} and Andreev. This feature is contrary to the inference that the interlayer coupling becomes strong if the number of CuO_2 planes in a unit cell increases. Also, the fluctuation-induced susceptibility in the low-field region was analyzed by using the modified Lawrence-Doniach model. The effective number of independently fluctuating CuO_2 layers per unit cell, g_{\rm eff}, turned out to be \simeq 2 rather than 4, which indicated that two among the four CuO_2 layers were in states far from their optimal doping levels. This result could explain why CuBa_{2}Ca_{3}Cu_4O_{12-\delta} shows two-dimensional behavior.