In two-dimensional electronic systems, direct first-order phase transitions are prohibited as a consequence of the long-range Coulomb interaction, which implies a stiff energetic penalty for macroscopic phase separation. A prominent proposal is that any direct first-order transition is instead replaced by a sequence of “microemulsion” phases, in which the two phases are mixed in patterns of mesoscopic domains. In this Letter, we comment on the range $\mathrm{\Delta }n$ of average electron density that such microemulsion phases may occupy. We point out that, even without knowing the value of a phenomenological parameter associated with surface tension between the two phases, one can place a fairly strong upper bound on the value of $\mathrm{\Delta }n$. We make numerical estimates for $\mathrm{\Delta }n$ in the case of the Fermi liquid to Wigner crystal transition and find $\mathrm{\Delta }n$ to be on the order of ${10}^7$ ${\mathrm{cm}}^{-2}$. This value is much smaller than the width of the phase transition observed in experiments, suggesting that disorder is a more likely explanation for the apparent broadening of the transition.

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• Exotic phases of matter
• Quantum phase transitions
• Quantum fluids & solids
• Strongly correlated systems
• Two-dimensional electron system
• Wigner crystal