A simple model for the metal-insulator transition in a two-dimensional electron gas

TL;DR

This paper presents a simple, self-consistent electrostatic model for a 2D electron gas that predicts a threshold density for the insulator-metal transition, aligning well with experimental observations.

Contribution

It introduces a novel elementary model accounting for perpendicular electron tunneling effects in 2D systems, predicting transition thresholds consistent with experiments.

Findings

Predicted threshold density matches experimental data

Model explains the insulator to quasi-metallic transition

Highlights importance of perpendicular tunneling in 2D electron gases

Abstract

We introduce an elementary model for the electrostatic self-consistent potential in a two-dimensional electron gas. By considering the perpendicular degree of freedom arising from the electron tunneling out of the system plane, we predict a threshold carrier density above which this effect is relevant. The predicted value agrees remarkably well with the onset for the insulator to quasi-metallic transition recently observed in several experiments in SiO2-Si and AlGaAs-GaAs heterojunctions.