Percolation-type description of the metal-insulator transition in two dimensions

TL;DR

This paper introduces a non-interacting-electron model combining quantum tunneling and classical percolation to explain various experimental features of the two-dimensional metal-insulator transition, emphasizing the role of dephasing.

Contribution

It presents a simple percolation-based model that accounts for key experimental observations of the 2D metal-insulator transition without invoking electron interactions.

Findings

Resistance exhibits exponential temperature dependence on the metallic side.

Critical resistance is on the order of e^2/h.

Metallic phase is suppressed by a parallel magnetic field.

Abstract

A simple non-interacting-electron model, combining local quantum tunneling and global classical percolation (due to a finite dephasing time at low temperatures), is introduced to describe a metal-insulator transition in two dimensions. It is shown that many features of the experiments, such as the exponential dependence of the resistance on temperature on the metallic side, the linear dependence of the exponent on density, the $e^2/h$ scale of the critical resistance, the quenching of the metallic phase by a parallel magnetic field and the non-monotonic dependence of the critical density on a perpendicular magnetic field, can be naturally explained by the model.