Nonlinear screening and percolative transition in a two-dimensional electron liquid

TL;DR

This paper introduces a new variational method to analyze the percolation threshold, structure, and compressibility of disordered 2D electron liquids, revealing that the metal-insulator transition occurs before percolation.

Contribution

A novel variational approach providing high-accuracy predictions for percolation and thermodynamic properties in disordered 2D electron liquids.

Findings

Inverse compressibility has a strongly asymmetric minimum.

Metal-insulator transition occurs before the percolation threshold.

Method verified against numerical results and asymptotics.

Abstract

A novel variational method is proposed for calculating the percolation threshold, the real-space structure, and the thermodynamical compressibility of a disordered two-dimensional electron liquid. Its high accuracy is verified against prior numerical results and newly derived exact asymptotics. The inverse compressibility is shown to have a strongly asymmetric minimum at a density that is approximately the triple of the percolation threshold. This implies that the experimentally observed metal-insulator transition takes place well before the percolation point is reached.