Hall effect near the vortex-glass transition in high-temperature superconductors

We discuss the Hall effect in the mixed state of type-II superconductors with an emphasis on the regime near the vortex-glass transition. This transition is argued to have a ‘‘hidden’’ particle-hole symmetry, and a new exponent is introduced to characterize the irrelevance of the particle-hole asymmetry. This leads to a natural explanation of the scaling of the Hall and Longitudinal resistivities observed in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. At the transition, the nonlinear Hall voltage is predicted to vary with a universal power of the current, and the linear ac Hall conductivity with a universal power of the frequency.