Superclimb of Dislocations in Solid $^4$He*

Edge dislocation with superfluid core can perform {\it superclimb} -- non-conservative motion (climb) assisted by superflow along its core. Such dislocation, with Burgers vector along the C-axis, has been found in {\it ab initio} simulations of {\it hcp} solid $^4$He [1]. Uniform network of superclimbing dislocations can induce {\it isochoric compressibility} $\chi = dN/d\mu $ which is finite (in contrast to ideal solid where it vanishes) and, practically, independent of the network density. Here $N$ is total number of atoms and $\mu$ is chemical potential [1]. Such giant response has been observed by Ray and Hallock during superfluid flow events through solid He4 [2]. Study [3] of superclimbing dislocation within the model of Granato-L\"ucke string, subjected to Peierls potential and to vanishing bias by $\mu$, has found that $\chi$ exhibits wide peak in the intermediate range of temperatures (T) - above some $T_p$ determined by Peierls energy and below $T_s \sim 0.5$K above which superfluidity of the core essentially vanishes. Non-Luttinger type behavior characterized by $\chi \sim L^b$ scaling as some power $1< b \leq 2$ of dislocation length $L$ is observed in the wide peak region. Biasing superclimbing dislocation by finite $\mu$ (due to a contact with liquid $^4$He through vycor electrodes [2],[4]) can induce core roughening caused by thermally assisted tunneling of jog-antijog pairs through the barrier produced by combination of Peierls potential and the bias [5]. The threshold for this effect scales as $\mu_c\sim 1/L^a$ with some power $a\approx 1.7$. The roughening is found to be hysteretic below some temperature $T_{\rm hyst}$. At $T_{\rm hyst}< T < T_R$, with $T_R$ determining temperature of thermal roughening, $\chi$ exhibits strong and narrow resonant peak leading to a dip in the core superfluid sound velocity. This mechanism is proposed as an explanation for a strong and narrow dip observed in critical superflow rate [4]. It is found that the dip characteristics are sensitive to the bias by $\mu$ and, therefore, this can be used as a test for the proposed mechanism. It is also predicted that the dip depth at given $T$ should be periodic in $\mu$ with the period $\sim \mu_c$. \\[4pt] [1] S. G. S\"oyler, et. al., PRL {bf 103}, 175301 (2009).\\[0pt] [2] M. W. Ray and R. B. Hallock, PRL {\bf 100}, 235301 (2008) ; PRB {\bf 79}, 224302 (2009); PRB {\bf 81}, 214523 (2010); Phys. Rev. {\bf B82}, 012502 (2010);\\[0pt] [3] D. Aleinikava, et al., JLTP, to be published;\\[0pt] [4] M. W. Ray and R. B. Hallock , Phys. Rev. Lett. {\bf 105}, 145301 (2010); \\[0pt] [5] D. Aleinikava and A.B. Kuklov, unpublished.