Superfluid fraction tensor of a two-dimensional dipolar supersolid
In plain words
In a supersolid only part of the matter flows freely (the superfluid fraction). It has been measured in a chain of droplets, but not in a two-dimensional crystal where it can depend on direction.
Precise statement
For a 2D triangular or honeycomb supersolid of Dy-164 or Er-166, measure the superfluid fraction tensor f_s,ij (via Josephson oscillations, moment of inertia or sound speeds) as a function of density contrast, and compare with Leggett's upper and lower bounds computed from the measured density profile. Answer: f_s,ij versus contrast with errors.
What would settle it
A 2D measurement of $f_s$ along two lattice directions compared with Leggett bounds from in-situ imaging.
Status in the literature
Unverified note
A 2024 Josephson-effect measurement in a one-dimensional droplet array found a sub-unity fraction consistent with the Leggett bound (Biagioni et al., Nature 2024; arXiv:2311.04757).