Intermediate phases of the two dimensional electron fluid between the Fermi liquid and the Wigner crystal

Abstract

We show that there can be no direct first order transition between a Fermi liquid and an insulating electronic (Wigner) crystalline phase in a clean two-dimensional electron gas in a metal-oxide-semiconductor field-effect transistor (MOSFET); rather, there must always exist intermediate ``micro-emulsion'' phases, and an accompanying sequence of continuous phase transitions. Among the intermediate phases which we find are a variety of electronic liquid crystalline phases, including stripe-related analogues of classical smectics and nematics. The existence of these phases can be established in the neighborhood of the phase boundaries on the basis of an {\it asymptotically exact} analysis, and reasonable estimates can be made concerning the ranges of electron densities and device geometries in which they exist. They can occur in clean Si MOSFETs in the range of densities in which an ``apparent metal to insulator transition'' has been observed in existing experiments. We also point out that, in analogy with the Pomaranchuk effect in $^3$He, the Wigner crystalline phase has higher spin entropy than the liquid phase, leading to an increasing tendency to crystallization with increasing temperature.