Universal temperature dependence of the mass flux in solid helium

The flux, $F$, carried by solid $^4$He, with nominal 300 ppb $^3$He concentration, $\chi$, in the range 25.6 - 26.3 bar rises with falling temperature and at a temperature $T_d$ the flux decreases toward zero [1]. The behavior of the flux above $T_d$ demonstrates the presence of a bosonic Luttinger liquid [2]. We study $F$ as a function of $^3$He concentration $\chi$ for $T > $ $T_d$ to explore the effect of $^3$He on the temperature dependence of $F$. We find that $F$ is sample-dependent and that the temperature dependence of $F$ above $T_d$ is universal; data for all samples scales to collapse on a universal curve. The universal behavior extrapolates to zero flux in the vicinity of $T_h$ $\approx$ 610 mK. With increases in temperature, an activated process degrades the flux. One possibility is the presence of kinks on dislocation cores, which would introduce disorder and introduce phase slips. \\[4pt] [1] M.Ray and R.B. Hallock, PRL 105, 145301 (2010); PRB 84, 144512 (2011).\\[0pt] [2] Ye. Vekhov and R.B. Hallock, PRL 109, 045303 (2012).