Kötzler et al. Reply: The Comment [1] picks up two features of our Letter [2] and proposes alternative interpretations of both in terms of results for the 2D XY model [3]. In this Reply, we argue that our key conclusion, i.e., the loss of superconducting (SC) phase coherence via a thickness-induced vortex-loop (VL) unbinding at T ? d below the virtual 3D bulk transition T c [see Fig. 1(a)], is not weakened by the given reasons. The other point of the Comment addresses the onset of SC phase fluctuations observed in the dynamical conductance (see Fig. 1) at temperatures T ! > T c . Here we agree that 2D vortexantivortex (v=a) fluctuations in partially coupled CuO 2 planes are operative; however, we provide evidence against 2D XY, i.e., Kosterlitz-Thouless(KT) -type ordering effects, as emphasized in the Comment.We follow the order of the Comment and first discuss the onset phenomena. There we assumed a dynamical scaling function S ! to fit the larger, inductive component of the conductance, i.e., !G 00 !. As shown by Fig. 1 of Ref.[1] for d 100 nm, the Kronig-Kramers transform of !G 00 underestimates the loss component !G 0 . We observe this enhancement of the !G 0 peak on rather homogeneous (from AFM images) films , such as d 50 nm ( 1) shown in Fig. 1, as well as on more inhomogeneous ones ( 0:4). Upon decreasing homogeneity, the normalized !G 0 peaks broaden and decrease to below 1=. We, therefore, suspect that the film disorder affects the dynamical shape. We should emphasize, however, that our main conclusion was drawn from the leading quantities, i.e., the peak temperatures T ! . They clearly reveal an Arrhenius-type behavior of the phase relaxation time T, the barriers of which could be associated with the nucleation of vortex cores. There and also in the experimental literature discussed in Ref.[2], no indication is seen for cooperative KT, i.e., v=a binding features, as inferred in the Comment. We cannot exclude that such effects occur closer to T c of our films; however, there is no evidence at the present frequencies.Within the KT scenario, phase coherence is expected below the virtual ordering temperature T KT d < T c , and Medvedyeva et al.[1] take our ''universal'' inverse kinetic conductance L ÿ1 k Td 35 nH ÿ1 to validate their interpretation. However, since they do not provide any argument for the huge, i.e., 500%, difference to the universal KT value of L ÿ1 k T KT d 7 nH ÿ1 , this interpretation is yet unjustified. Moreover, we have obtained from the universal value the c-axis coherence lengths for all our films, c T ? 0:4d. This constitutes our strong evidence for the thickness-induced vortex-loop unbinding, since d varied by more than 1 order of magnitude and c T measures the mean VL (loop) diameter. Note that the ratio c =d has been extracted from data, rather than introduced as an additional condition, as claimed in the Comment. Moreover, the number c T ? =d 0:4 is fully consistent with the values 0.3 and 1.0 obtained from data
