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We study the distribution of transport current across superconductingBi$_2$Sr$_2$CaCu$_2$O$_8$ crystals and the vortex flow through the sampleedges. We show that the $T_x$ transition is of electrodynamic rather thanthermodynamic nature, below which vortex dynamics is governed by the edgeinductance instead of the resistance. This allows measurement of the resistancedown to two orders of magnitude below the transport noise. By irradiating thecurrent contacts the resistive step at vortex melting is shown to be due toloss of c-axis correlations rather than breakdown of quasi-long-range orderwithin the a-b planes.

Transport Properties of Vortex Matter Governed by the Edge Inductance of Superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ Single Crystals