Berry phases and the intrinsic thermal Hall effect in high temperature cuprate superconductors
Abstract
The Bogoliubov quasiparticles move in a practically uniform magnetic field in the vortex state of high temperature cuprate superconductors. Do the quasiparticles experience a Lorentz force when set in motion by an externally applied heat current jQ, bending their trajectories and causing the temperature gradient perpendicular to jQ and the applied field H, or is the thermal Hall effect a consequence of Berry phases as in an intrinsic anomalous Hall effect of a semiconductor/metal with spin-orbit coupling? Here we show that it is the latter, and for the first time, calculate the temperature, H-field and the d-wave pairing gap dependence of the intrinsic thermal Hall conductivity, xy. We find that the intrinsic contribution to xy displays a rapid onset with increasing temperature, which compares favourably with existing experiments at high H-fields on the highest purity samples. This finding may help to settle a much-debated question of the bulk value of the pairing strength in cuprate superconductors in magnetic field.