Two-Dimensional Fluctuations Close to the Zero-Field Transition of Bi₂Sr₂CaCu₂O₈

The ac-conductivity along the CuO$_2$-layers of epitaxial films and single crystals of thicknesses 0.2$\mu$m$\leq L_z \leq130\mu$m reveals clear signatures for 2D-ordering. In particular, at $T_c$ the screening length assumes the universal value $L_z\Lambda_{T_c}/2\nu_s$ predicted by the Kosterlitz-Thouless theory, which indicates that binding of long vortex strings nucleates long-range superconductivity in the present samples containing up to $10^5$ CuO$_2$-layers. Several details of the order-parameter dynamics remain unexplained.