Observation of two-dimensional vortices in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$

We report transport measurements in the mixed state of single crystals of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{x}}$ using a modified version of the dc flux transformer geometry pioneered by Giaever in low-${\mathit{T}}_{\mathit{c}}$ materials. We find that over a wide range of the phase diagram the vortices are effectively two dimensional in character. Our results suggest that vortex cutting is an efficient process and that it is unlikely that the vortices are strongly entangled in this region of the phase diagram.