Sign reversal of the Hall effect in untwinned single-crystal superconductingYBa2Cu3O7−δ

For untwinned single-crystal ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ in a magnetic field H, we find that the in-plane Hall conductivity ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$ just below the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ is the sum of two terms, ${\mathit{C}}_1$/H and ${\mathit{C}}_2$H, where ${\mathit{C}}_1$ and ${\mathit{C}}_2$ are field independent, in agreement with recent theoretical predictions of Dorsey et al. and Kopnin et al. ${\mathit{C}}_1$ and ${\mathit{C}}_2$ have opposite signs, as required by the observation that the Hall effect changes sign as the applied field is varied. ${\mathit{C}}_1$ is proportional to ${\mathrm{\tau }}^2$, and ${\mathit{C}}_2$ is approximately proportional to τ, where τ=(${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$, so the crossover field ${\mathit{H}}_0$, where ${\mathrm{\sigma }}_{\mathit{x}\mathit{y}}$=0, is proportional to ${\mathrm{\tau }}^{1/2}$.