On the Colloidal Phase of the Homogeneous Electron Fluid

TL;DR

This paper proposes that the homogeneous electron fluid exhibits a colloidal phase with complex transitions between crystal, fluid, and sol states, supported by theoretical arguments and connections to numerical findings.

Contribution

It introduces the concept of a colloidal phase in the electron fluid and explores its properties, including the existence of finite crystallites and their role in quantum phase transitions.

Findings

Colloidal phase separates Wigner crystal from high-density fluid.

Existence of finite crystallites with negative surface tension in 2D and 3D.

Quantum remnants of crystallites explain gapless excitations.

Abstract

We provide semi-rigorous arguments that the Homogeneous Electron Fluid (HEF) has a colloidal phase separating the Wigner Crystal from the high density fluid phase. Near the crossover between crystal and fluid ground state energies, the argument is quite general and valid for practically any quantum transition between a crystal and a more amorphous phase. In this regime, the colloid is a gel and its "Goldstone" modes are flows of irregular fluid droplets separated by crystalline walls. A metal insulator transition occurs when a single bubble of fluid spans the entire system. Beyond this transition the colloid is a sol and its properties depend on the existence of meta-stable finite crystallites with negative surface tension. If these exist, the sol phase has lower energy than the homogeneous fluid. In the two dimensional HEF, Kivelson and Spivak argued that such negative surface tension objects always exist, at least in the form of stripes. We argue that the existence of stripes also implies the existence of finite negative tension elliptical crystallites and the detailed competition between the finite crystallite phase and striped phases is difficult to calculate. We also provide weaker arguments that finite crystallites exist in three dimensions. This provides evidence for our claim that the gapless excitations at non-zero wavenumber, observed in the numerical calculations of\cite{haule}\cite{gapless} are quantum remnants of these crystallites (Bosonic quasi-particles) in the limit of vanishing surface tension. Finally, we suggest a Landau mean field theory for the second order quantum phase transition between the fluid and sol phases.