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

The magnetization of the four-layer superconductor CuBa 2 Ca 3 Cu 4 O 12 − δ with T c ≃ 117 K is presented. The high-field magnetization around T c ( H ) follows the exact two-dimensional scaling function given by Teˇsanovi´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 eff , turned out to be ≃ 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 4 O 12 − δ shows two-dimensional behavior.