Thermal conductivity and thermal Hall effect from vortex motion

In the mixed state of type-II superconductors the motion of vortices in response to an applied temperature gradient $\nabla T$ leads to a longitudinal and a transverse heat current along $\nabla T$ and $\nabla T\times \mathbf{B},$ respectively, where $\mathbf{B}$ is the magnetic field. We calculate the corresponding contributions to the thermal conductivity and the thermal Hall effect in terms of other thermomagnetic transport coefficients and the electrical resistivity. The vortex contribution to the thermal Hall effect may be observable in superconductors with weak pinning and small quasiparticle thermal conductivity.