Giant isochoric compressibility of solid He4 due to superclimb of dislocations*

In the experiment on superfluid transport in solid He4 [PRL {\bf 100}, 235301 (2008)], Ray and Hallock observed an {\it anomalously large isochoric compressibility}: the supersolid samples demonstrated a significant and apparently spatially uniform response of density and pressure to chemical potential $\mu$, applied locally through Vycor ``electrodes.'' We propose that the effect is due to {\it superclimb}: edge dislocations can climb because of mass transport along superfluid cores and, as a result, the crystal can accumulate extra matter which is, practically, independent of the dislocation density, provided it is uniform. We corroborate this scenario by {\it ab initio} simulations of an edge dislocation in solid He4 at $T=0.5K$ with Burgers vector along the C-axis: its superfluid core (split into partials) climbed in response to changes of $\mu$ [1]. At low $T$ the effect must be suppressed due to a crossover to the smooth dislocation, with the temperature scale determined by the energy of jog-antijog pair. \\[4pt] [1] \c{S}.G. S\"{o}yler, A. B. Kuklov, L. Pollet, N. V. Prokof'ev, and B. V. Svistunov , Phys. Rev. Lett. {\bf 103}, 175301 (2009).