Finite-temperature phase diagram of a two-dimensional supersolid
In plain words
In two dimensions, heat destroys perfect crystal and superfluid order, leaving only slowly decaying versions. How these two partial orders melt, together or one after another, is unknown.
Precise statement
Infinite 2D dipolar Bose gas in its supersolid regime at $T > 0$. Crystal and phase order are at most quasi-long-range. Classify the sequence of transitions (Berezinskii-Kosterlitz-Thouless superfluid loss, dislocation-mediated melting, possible hexatic or modulated-superfluid intermediate phases) with their critical behavior. Answer: phase diagram in ($T, a_s/a_{dd}$, density).
What would settle it
Finite-temperature simulations (for example path-integral Monte Carlo) of the 2D dipolar gas with scaling analysis, confirmed by measured correlation functions.
Status in the literature
Unverified note
2D supersolid arrays have been made since 2021 (Norcia et al., Nature 2021) and a 2D stripe supersolid in Er was reported in 2025 (arXiv:2512.13280); no measurement or simulation has resolved the finite-T transition sequence.