%e report on transport measurements in the mixed state of YBa2Cu307 single crystals using the dc flux transformer geometry. In the vortex fluid regime we have observed the onset of a nonlocal conductivity. At lower temperatures, close to but above the phase transition temperature the vortices become eA'ectively three dimensional in character. This is in sharp contrast to recent flux transformer experiments on Bi2Sr2CaCupO which have failed to see a nonlocal conductivity, confirming the twodimensional character at high temperatures of the vortices in that system. These observations suggest that in a finite temperature interval, the vortex state in YBa2Cu307 is a line liquid.The magnetic phase diagram of the oxide superconductors is a rich system with many novel physical phenomena playing a significant role. Effects such as thermal Auctuations, disorder, anisotropy, and dimensionality are all important in explaining the experimentally observed behavior [1]. It is now clear from experiments that there is a phase transition in the mixed state which separates a low temperature ordered phase from a high temperature vortex fluid. In the limit of strong pinning disorder, this low temperature phase appears to be a vortex glass [2] and the phase transition is known to be second order [3].In the weak pinning limit, the low temperature phase is a vortex lattice with long-ranged positional order and the transition is theoretically [41 and experimentally [5] found to be first order. However, there remain many open and important questions regarding the role of the dimensionality of the vortices.In a layered superconductor with the magnetic field perpendicular to the layers, one may ask whether the vortices in the different layers will tend to align forming vortex lines. This should occur when the interactions between vortices in adjacent layers are not overwhelmed by either thermal Auctuations or random pinning in the layers [2,6]. When the vortices do form lines this reAects strong correlations between layers and so the material is behaving three dimensionally.However, as the temperature is increased, the thermal Auctuations may destroy the correlations between layers [7], breaking the vortex lines up into point or "pancake" vortices in each layer [81 and causing a crossover to two-dimensional behavior. In YBa2Cu307 (YBCO) this crossover occurs in the vortex liquid regime and can be studied in a new way using multiterminal transport measurements as reported and analyzed in this Letter.In this paper, we present transport measurements on YBCO in the vortex liquid regime using the modified dc Aux transformer geometry [9]. We show that the data are highly inconsistent with the material being simply an anisotropic, local conductor. Thus we report the first observation of nonlocal conductivity in the mixed state of an 1272 oxide superconductor. This observation allows us to "measure" the vortex dimensionality as a function of temperature and directly show that at a temperature close to but above the vortex phase transition temperatu...
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