Giant isochoric compressibility of solid ${}^4\mathrm{He}$: The bistability of superclimbing dislocations

A significant accumulation of matter in solid ${}^4\mathrm{He}$ observed during a superflow event, dubbed the giant isochoric compressibility (or the syringe effect), is discussed within the model of dislocations with superfluid core. It is shown that solid ${}^4\mathrm{He}$ in contact with a superfluid reservoir can develop a bistability with respect to the syringe fraction, with the threshold for the bias by chemical potential determined by a typical free length of dislocations with superfluid core. The main implications of this effect are hysteresis and strongly nonlinear dynamical behavior leading to growth, proliferation, and possibly exiting from a crystal of superclimbing dislocations. Three major channels for such dynamics are identified: (i) injection and inflation of the prismatic loops from the boundary, (ii) Bardeen-Herring generation of the loops in the bulk, and (iii) helical instability of the screw dislocations. It is argued that the syringe instability may have already been observed in the experiments on the superflow through solid Helium-4. Several testable predictions for the time and the bias dependencies of the dynamics are suggested.

Figure 1

A forest of screw dislocations containing edge superclimbing segments. Dashed and solid lines indicate pure screw and pure edge segments, respectively, all characterized by the Burgers vector along the hcp axis.

Figure 2

A prismatic loop (solid line) generated by an edge segment AB, from Fig. 1, according to the Bardeen-Herring mechanism: An originally straight edge segment AB (solid horizontal line) bows under the bias (dashed-double-dotted line). Then further bowing results in the overhangs (dashed-dotted line). Points C and ${\text{C}}^{\prime }$ in the overhangs approach each other and eventually the whole prismatic loop detaches from points A and B.

Figure 3

Sketch of the growing superclimbing dislocation (dashed line). The area to its left indicates either building of extra plane of atoms or dissolving of the existing plane (not shown) between the upper and lower ones.

Figure 4

Geometry of the growing superclimbing dislocation (dashed line) sketched in Fig. 3. The end points of the dislocation are in a contact with the superfluid reservoir. The (solid) area under the curve indicates either the injected extra matter leading to the formation of new basal layer (actually two of them in hcp) or a removed part of the existing one.