Thermal Hall Conductivity of High Temperature Superconductors: Quantization and Scaling

Presented is the theory of thermal Hall conductivity ${\kappa }_{xy}$ in the vortex state of high temperature cuprate superconductors in the clean limit. We show that ${\lim }_{T\to 0}{\kappa }_{xy}\mathrm{/}T$ is a {\em staircase} function of 1/B with an envelope that scales as 1/B. The relation to the experiments is discussed.