Thermoelectric effects in anisotropic superconductors

We discuss the thermally generated magnetic flux in an anisotropic, homogeneous bulk superconductor. A previous calculation by Ginzburg is generalized to allow for large variations in the superelectron density $n_s$ between the hot and cold ends of the sample. Such variations arise when the temperature of the hot end is very near $T_c$, where the thermomagnetic field penetrating the sample $H\sim n_s^{-2\mathrm{}}\sim {(T_c-T)}^{-2\mathrm{}}$ is maximized. As a result of the nonuniformity of $H$, the total (integrated) magnetic flux is not necessarily quadratic in the temperature gradient as predicted by Ginzburg and Zharkov, but, in fact, is approximately linear in the regime of experimental interest. The derivation of a simple expression for the total flux follows from the conventional assumption that normal and supercurrents cancel ($\overrightarrow{\mathrm{j}}={\overrightarrow{\mathrm{j}}}_n+{\overrightarrow{\mathrm{j}}}_s\to 0$) within the bulk. We critically examine this assumption by calculating the actual net current density $\overrightarrow{\mathrm{j}}$ that does exist in the bulk, and the resulting corrections to $H$ and the total flux. The approximation $\overrightarrow{\mathrm{j}}=0\mathrm{}$ is valid as long as $T_c-T$ is greater than 1 or 2 mK. Otherwise, screening current persists sufficiently far into the sample that it must be taken into account when evaluating the total flux. The bulk current is also nonzero, but its effect on the flux is dominated by screening current. Finally, problems associated with the measurement of the flux are discussed.