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The Bogoliubov quasiparticles move in a practically uniform magnetic field inthe vortex state of high temperature cuprate superconductors. Do thequasiparticles experience a Lorentz force when set in motion by an externallyapplied heat current ${\bf j}_Q$, bending their trajectories and causing thetemperature gradient perpendicular to ${\bf j}_Q$ and the applied field ${\bfH}$, or is the thermal Hall effect a consequence of Berry phases as in anintrinsic anomalous Hall effect of a semiconductor/metal with spin-orbitcoupling? Here we show that it is the latter, and for the first time, calculatethe temperature, ${\bf H}$-field and the $d$-wave pairing gap $\Delta$dependence of the intrinsic thermal Hall conductivity, $\kappa_{xy}$. We findthat the intrinsic contribution to $\kappa_{xy}$ displays a rapid onset withincreasing temperature, which compares favourably with existing experiments athigh ${\bf H}$-fields on the highest purity samples. This finding may help tosettle a much-debated question of the bulk value of the pairing strength incuprate superconductors in magnetic field.

Berry phases and the intrinsic thermal Hall effect in high temperature cuprate superconductors