Mass Superflux in Solid Helium: the Role of $^3$He Impurities

Below $\sim 630$~mK, the \4he atom mass flux, $F$, that passes through a cell filled with solid hcp \4he in the pressure range 25.6 - 26.4~bar, rises with falling temperature and at a temperature $T_d$ the flux drops sharply. The flux above $T_d$ has characteristics that are consistent with the presence of a bosonic Luttinger liquid. We study $F$ as a function of $^3$He concentration, $\chi = 0.17 - 220$~ppm, to explore the effect of $^3$He impurities on the mass flux. We find that the strong reduction of the flux is a sharp transition, typically complete within a few mK and a few hundred seconds. Modest concentration-dependent hysteresis is present. 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 for $T_{ps}$ \emph{vs.} $\chi$. We conclude that $^3$He plays an important role in the flux extinction. The dependence of $F$ on the solid helium density is also studied. We find that $F$ is sample-dependent, but that the temperature dependence of $F$ above $T_d$ is universal; data for all samples scales and collapses to a universal temperature dependence, independent of $^3$He concentration or sample history. The universal behavior extrapolates to zero flux in the general vicinity of $T_h \approx 630$~mK. With increases in temperature, it is possible that a thermally activated process contributes to the degradation of the flux. The possibility of the role of disorder and the resulting phase slips as quantum defects on one-dimensional conducting pathways is discussed.