Thermal Hall effect in the underdoped cuprate superconductor YBa$_2$Cu$_3$O$_{6.5}$*

The thermal Hall conductivity $\kappa_{xy}$ (Righi-Leduc effect) is tailor-made to probe the transport properties of Bogolyubov quasiparticles (QPs) in a superconductor because neither the phonons nor vortices contribute to the off-diagonal response. We report measurements of $\kappa_{xy}$ in untwinned crystals of underdoped YBa$_2$Cu$_3$O$_{6.5}$, extending from 100 K to 15 K in fields $H$ up to 14 T. Several key features will be described. At all temperatures $T$, the QPs are hole-like. However, there is a small negative contribution that appears just below $T_c$. Below 30 K, the curve of $\kappa_{xy}/T$ vs. $H$ approaches an apparent universal step-like profile that may reflect the behavior of long-lived Dirac excitations confined to orbits around the gap nodes in an intense magnetic field. Measurements to much lower $T$ and higher $H$ ($\sim$ 32 T) are planned.