How does the field-induced Wigner crystal melt into quantum Hall liquids?
In plain words
A strong perpendicular magnetic field shrinks electron orbits and favors a crystal at low filling, but fractional quantum Hall liquids compete with it. How the system passes between the two, and whether unusual intermediate states appear, is open.
Precise statement
In high-mobility GaAs and graphene 2D systems at Landau-level filling $\nu$ between $1/7$ and $1/3$, insulating phases interpreted as pinned Wigner crystals reenter between fractional quantum Hall states, e.g. near $\nu = 1/5$. Determine the $T = 0$ phase diagram in $(\nu, r_s)$ including Landau-level mixing, the order of the crystal to liquid transitions, and whether intermediate phases (Hall crystals, crystals of composite fermions) exist.
What would settle it
Local imaging and thermodynamic measurements across $\nu$ near $1/5$, matched to variational or DMRG calculations that include Landau-level mixing.
Status in the literature
Unverified note
Scanning tunneling microscopy in Bernal bilayer graphene directly imaged a magnetic-field-induced Wigner crystal (Tsui et al., Nature 628, 287, 2024); its transitions to neighboring quantum Hall liquids are under study.