Quantized thermal Hall effect in the mixed state of d-wave superconductors.

We consider quasiparticles of a clean d-wave superconductor in the vortex lattice state. For vortex lattices that are inversion symmetric, the quasiparticle bands are found to have a Dirac cone dispersion at zero energy, within the linearized approximation. Upon going beyond the linearized approximation by including the effect of the smaller curvature terms, the Dirac cone dispersions acquire a small gap that scales linearly with the applied magnetic field ( approximately 0.5 K T(-1) in YBa2Cu3O6.9). When the "chemical potential" for quasiparticles lies within the gap, quantization of the thermal Hall conductivity, kappa(xy)/T = n(pi(2)k(2)(B)/3h), with n = +/-2,0, is predicted at low temperatures.