Angle-dependent magnetothermal conductivity in d-wave superconductors

We analyse the behavior of the thermal conductivity, $\kappa (H)$, in the vortex state of a quasi-two-dimensional d-wave superconductor when both the heat current and the applied magnetic field are in the basal plane. At low temperature the effect of the field is accounted for in a semiclassical approximation, via a Doppler shift in the spectrum of the nodal quasiparticles. In that regime $\kappa (H)$ exhibits twofold oscillations as a function of the angle between the direction of the field in the plane and the direction of the heat current, in agreement with experiment.