Stress induced roughening of superclimbing dislocation in solid $^4$He

We investigate numerically superclimb [1] of dislocation in solid $^4$He biased by externally imposed chemical potential $\mu$. The effective action takes into account quantum phase slips in the core superfluid as well as the core displacement in Peierls potential within the Granato-L\"{u}cke string model. The bias produces stress on the core and this can result in dislocation roughening. Such roughening is characterized by hysteretic behavior at temperatures (T) below some threshold $T_{\rm hyst}$. At $T>T_{\rm hyst}$ strong resonant peaks develop in the dislocation differential response. These peaks exhibit periodic behavior vs $\mu$, with the period determined by Peierls potential and dislocation length. We explain these effects by thermally assisted tunneling of jog-antijog pairs across the barrier created by Peierls potential and the bias. Since superclimbing is controlled by core superflow, speed of sound along the superfluid core exhibits dip-like features at the peak positions. We propose that this effect is seen in the mass transport experiment [2].\\[4pt] [1] S. G. S\"{o}yler, et al, Phys. Rev. Lett. {\bf 103}, 175301 (2009).\\[0pt] [2] M. W. Ray and R. B. Hallock, Phys. Rev. Lett. {\bf 105}, 145301 (2010).