Luttinger Liquid in the Core of a Screw Dislocation in Helium-4

On the basis of first-principles Monte Carlo simulations we find that the screw dislocation along the hexagonal axis of an hcp ${}^4\mathrm{He}$ crystal features a superfluid (at $T\to 0$) core. This is the first example of a regular quasi-one-dimensional supersolid—the phase featuring both translational and superfluid orders, and one of the cleanest cases of a Luttinger-liquid system. In contrast, the same type of screw dislocation in solid ${\mathrm{H}}_2$ is insulating.

Figure 1

(For the best perception, look from a distance.) Columnar winding-cycle map (blue or small gray dots) in the core of the screw dislocation in solid ${}^4\mathrm{He}$ at $T=0.25\mathrm{K}$ and density $0.0287{\AA }^{-3}$. View is along the hexagonal axis, with the core parallel to it. Shown with red dots (or dark circles) (in the lower half of the plot only) are the atomic positions in the initial configuration. At distances $\sim 3a$ from the core, the atomic positions averaged over the imaginary time are only slightly shifted against those of the original configuration. The unit of length is 1 Å.

Figure 2

Columnar winding-circle map in the core of screw dislocation. View is along the $x$ axis in the basal plane—perpendicular to the core. Shown with red dots (or dark circles) (in the lower half of the plot only) are the atomic positions in initial configuration. The unit of length is 1 Å.