Upper bound on the window of density occupied by microemulsion phases in two-dimensional electron systems

TL;DR

This paper derives an upper bound on the density range of microemulsion phases in 2D electron systems, suggesting disorder, not microemulsions, likely explains experimental transition broadening.

Contribution

It provides a theoretical upper limit on the density span of microemulsion phases in 2D electron systems, independent of surface tension parameters.

Findings

Upper bound on density range is about 10^7 cm^-2.

The bound is much smaller than experimentally observed transition widths.

Disorder likely causes the broadening of the phase transition.

Abstract

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 note, we comment on the range $\Delta n$ 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 $\Delta n$. We make numerical estimates for $\Delta n$ in the case of the Fermi liquid to Wigner crystal transition and find $\Delta n$ to be on the order of $10^7$\,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.