Mass Superflux in Solid Helium: Dependence on Temperature, Density and $^3$He Impurity Concentration

The mass flux, $F$, induced to flow through solid $^4$He by means chemical potential differences imposed by the fountain effect in the range $25.6 < P< 26.4$~bar rises with falling temperature below ~650 mK. At a low temperature, $T_d$, the flux drops sharply. The behavior of the flux above $T_d$ is consistent with the presence of a bosonic Luttinger liquid. We report a study $F$ as a function of $^3$He concentration, $\chi$ $(0.17 - 220)$~ppm, and explore the effect of level of $^3$He impurities on $T_d$. We find a strong reversible reduction of the flux, typically complete within a few mK. We find that $T_d$ is an increasing function of $\chi$ and the $T_d(\chi)$ dependence differs somewhat from the predictions for bulk phase separation. It is possible that the cores of edge dislocations carry the flux. In such a case the flux may be extinguished by the decoration of the cores or dislocation intersections by $^3$He. We find that $F$ is sample-dependent, but that the temperature dependence of $F$ above $T_d$ is universal; data for all samples scale and collapse to a universal temperature dependence, independent of $^3$He concentration but with a weak pressure dependence. [Work supported by NSF DMR 12-05217.]