Are there intermediate phases between the Wigner crystal and Fermi liquid?
In plain words
Theory argues that with long-range Coulomb repulsion a sharp switch from liquid to crystal is impossible in two dimensions, so mixed phases of crystal bubbles or stripes should appear in between. Whether these microemulsion phases exist is disputed.
Precise statement
Spivak and Kivelson (2004) argued that a direct first-order transition is forbidden in 2D with $1/r$ interactions, which implies intermediate microemulsion phases (bubbles, stripes) in a window of $r_s$ near $r_s$_c. Determine whether these phases exist in clean 2D jellium and in gated devices where the interaction is screened beyond the gate distance d, their width in r_s, and their observable signatures (transport anisotropy, compressibility, local density images).
What would settle it
Equilibrium imaging (scanning tunneling or optical) of mesoscale crystal and liquid domains in a clean $2\mathrm{D}$ system as density is swept through r_s_c, with disorder shown to be too weak to pin them.
Status in the literature
Unverified note
Optical spectroscopy of a transition-metal dichalcogenide heterostructure claimed an intermediate electronic microemulsion phase (Sung et al., Nature Physics 21, 437, 2025); whether disorder rather than Coulomb frustration produces the coexistence is unresolved.