6533b852fe1ef96bd12ab5ce

RESEARCH PRODUCT

Vortex-liquid entanglement inBi2Sr2CaCu2O8+δfilms in the presence of quenched disorder

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We have investigated the thermally activated behavior of the in-plane electrical resistivity of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ films for magnetic fields $Bl~{10}^{4}\mathrm{G}$ applied parallel to the $c$ axis. The activation energy in the vortex-liquid state changes suddenly at a crossover field ${B}_{\mathrm{cr}}.$ The anisotropy reduction generated by oxygen annealing leads to the increase of the crossover field. For $Bl{B}_{\mathrm{cr}},$ the activation energy $U$ is weakly magnetic-field dependent. For $Bg{B}_{\mathrm{cr}},$ $U(B,T)\ensuremath{\sim}(1\ensuremath{-}{T/T}_{c0}{)/B}^{1/2},$ which corresponds to an entangled vortex fluid. The observation of vortex-liquid entanglement in the presence of relevant quenched disorder is discussed in connection with the relation between the theoretically predicted entanglement length for a clean system and the collective pinning length along the field direction. Our results suggests that, in the case of a pronounced anisotropy and significant collective pinning, the entanglement field ${B}_{E}{=B}_{\mathrm{cr}}\ensuremath{\approx}{\ensuremath{\Phi}}_{0}/{\ensuremath{\gamma}}^{2}{s}^{2},$ where $s$ is the interlayer spacing.