Supersolid State of Matter

We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, in the absence of symmetry between vacancies and interstitials, superfluidity has a zero probability to occur in commensurate solids which break continuous translation symmetry. We discuss recent ${}^4\mathrm{He}$ experiments by Kim and Chan in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid interfaces.

Figure 1

Particle world lines in different crystals at low temperature. The time axis is vertical. The dashed lines show the equilibrium lattice points. (a) Nearly classical crystal at low temperature; $\mathbf{M}=0$. (b) Insulating quantum crystal with large zero-point fluctuations and frequent particle exchange processes; $\mathbf{M}=0$. (c) Particle world lines with a nonzero winding number.

Figure 2

Evolution of the coarse-grained picture (see text) for a trajectory with a nonzero winding number similar to Fig. 1c. Solid and open circles show particle and lattice site positions correspondingly. Arrows indicate the direction of the particle-number current.