Diminishing sign anomaly and scaling behavior of the mixed-state Hall resistivity in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10}$ films containing columnar defects

The issues of sign reversal of the Hall voltage and scaling between longitudinal (${\mathrm{\rho }}_{\mathit{x}\mathit{x}}$) and Hall (${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$) resistivities are studied in ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{10}$ films in which the vortex dynamics is drastically changed by flux pinning at heavy-ion-irradiation–induced linear defects. While the sign anomaly diminishes with increasing defect concentration, the power law ${\mathrm{\rho }}_{\mathit{x}\mathit{y}}$∼${\mathrm{\rho }}_{\mathit{x}\mathit{x}}^{\mathrm{\beta }}$, β=1.85±0.1, holds even after irradiation. This result shows that the scaling is a universal feature of the mixed state in this system. The sign anomaly, on the other hand, is not consistent with a model that invokes pinning-induced backflow in the vortex core as the mechanism for this effect.