Thermomagnetic Effects in Dirty Type-II Superconductors

We reconsider microscopically and thermodynamically the heat current associated with the motion of vortex lines in a dirty type-II superconductor and show that the heat-current operator ${{\overrightarrow{\mathrm{j}}}_0}^h$ employed previously by Caroli and Maki has to be replaced by ${\overrightarrow{j}}^h$ in the presence of a constant magnetic field $H:{\overrightarrow{\mathrm{j}}}^h={{\overrightarrow{\mathrm{j}}}_0}^h+H{\overrightarrow{\mathrm{j}}}^M$, where ${\overrightarrow{\mathrm{j}}}^M$ may be called the magnetization current. We then recalculate the entropy associated with a single vortex line $S_D$ at all temperatures (and in the high-field region), which vanishes like $T$ at low temperatures.