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Reading the article [Rev. Mod. Phys. 84, 759 (2012)] by Prokof'ev and Boninsegni, a supersolid is defined as a homogeneous phase of matter in which both density long-range order (i.e. ordered spatial modulation) and off-diagonal long-range order (i.e. superfluidity) exist simultaneously and appear spontaneously for the same species of particles.

Then several exotic examples are proposed, including solid $^{4}\mathrm{He}$ and dipolar quantum gases.

In my opinion, a more basic supersolid system should simply be a crystal of quantum vortices in a superfluid, since there is both superfluidity and spatial order.

This kind of state spontaneously emerge upon rotating a superfluid sample. Why is this broad and easily-accessible family of seemingly supersolid systems completely neglected? Am I missing something?

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I think that it's probably because the spatial order due to the vortex lattice emerges at a scale (i.e. the typical distance between vortices) that is greater than the scale of ODLRO. At this scale the system is practically in a hydrodynamic regime, in the sense that QM is not needed to describe it. In fact, the Tkachenko waves (that are basically elastic waves in the Abrikosov lattice of the vortices) can be studied, and derived, with classical hydrodynamics.

Moreover, vortices are expected to exist in a supersolid, but, as far as I know, their possible Abrikosov lattice would not constitute an example of "supersolid-solid" (for the same reason given above). I'd rather say that it's the presence of vortices that inform you that you're observing a "super" state of matter, at least at a certain "mesoscopic" scale.

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