The effect of out-of-plane impurities on the thermal Hall conductivity $\kappa_{ xy}$ of in-plane marginal-Fermi-liquid (MFL) quasiparticles in high-$T_c$ cuprates is examined by following the work on electrical Hall conductivity $\sigma_{ xy}$ by Varma and Abraham [Phys. Rev. Lett. 86, 4652 (2001)]. It is shown that the effective Lorentz force exerted by these impurities is a weak function of energies of the MFL quasiparticles, resulting in nearly the same temperature dependence of $\kappa_{ xy}/T$ and $\sigma_{ xy}$, indicative of obedience of the Wiedemann-Franz law. The inconsistency of the theoretical result with the experimental one is speculated to be the consequence of the different amounts of out-of-plane impurities in the two YBaCuO samples used for the $\kappa_{ xy}$ and $\sigma_{ xy}$ measurements.
Categories: cond-mat.supr-con