Scaling of vortex-liquid resistivity in high-$T_c$ superconductors

Analysis of the in-plane resistivity of a ${\mathrm{Tl}}_2{\mathrm{Ba}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ thin film and of several oxygen-deficient $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ single crystals in magnetic fields $0⩽B⩽12\mathrm{T}$ applied along the crystallographic $c$ axis were performed to study the resistive transition into the glassy state. The transition curves were scaled according to a modified model for the vortex-liquid resistivity, finding good scaling only for fields below a certain value $B_0$, consistent with the field-induced crossover between a three-dimensional and quasi-two-dimensional regime of the vortex fluctuations reported in several works. This indicates that for low fields the vortex state is in fact three dimensional and provides further support to a coherent description of the vortex-liquid resisitivity.

Figure 1

Resistance of the ${\mathrm{Tl}}_2{\mathrm{Ba}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ thin film for magnetic fields (from right to left) $B=0$, 0.3, 0.5, 0.7, 1, 1.5, 2, 3, 4, 6, 8, 10, and 12 T. The straight line shows the estimation of the normal-state resistance. Inset: Glass temperature $T_g$ for all fields under study. The solid line is a fit to Eq. (3) with $B_0=1.53\mathrm{T}$ and $\beta =0.55$.

Figure 2

Scaling according to Eq. (4) for five magnetic fields in the range $0.3⩽B⩽1.5\mathrm{T}$, and also for $B=3$ and 10 T (arrows) for the Tl-2212 film.

Figure 3

Scaling according to Eq. (4) for different $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ single crystals with various oxygen content. Good scaling is found for fields below $B_0$. The arrows point to the curve corresponding to the lowest measured field in each case. For sample data, see Table .