Fluctuation phenomena in excess conductivity and magnetization of single-crystal ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathit{y}}$

We present an analysis of the measured excess conductivity which results from the fluctuation of the superconducting order parameter of a ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{y}}$ single crystal and found it was fit best by the two-dimensional Aslamazov-Larkin theory. The magnetoconductivity and magnetization studies are in good agreement with the two-dimensional (2D) scaling behavior in the fremework of Lawrence-Doniach model revealing the 2D nature of the fluctuation near the mean-field transition temperature in the presence of a field.