Two-species percolation and Scaling theory of the metal-insulator transition in two dimensions

TL;DR

This paper introduces a two-species percolation scaling theory based on a non-interacting-electron model to explain various experimental features of the metal-insulator transition in two-dimensional systems.

Contribution

The paper develops a novel two-species percolation model that successfully explains multiple experimental observations of the 2D metal-insulator transition.

Findings

Explains exponential resistance dependence on temperature on the metallic side.

Accounts for the critical resistance scale of e^2/h.

Matches the parallel magnetic field dependence of critical density with experiments.

Abstract

Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two dimensions [1]. Here, based upon that model, a two-species-percolation scaling theory is introduced and compared to the experimental data. The two species in this model are, on one hand, the ``metallic'' point contacts, whose critical energy lies below the Fermi energy, and on the other hand, the insulating quantum point contacts. 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. Moreover, details such as the nonmonotonic dependence of the resistance on temperature or the inflection point of the resistance vs. parallel magnetic are also a natural consequence of the theory. The calculated parallel field dependence of the critical density agrees excellently with experiments, and is used to deduce an experimental value of the confining energy in the vertical direction. It is also shown that the resistance on the ``metallic'' side can decrease with decreasing temperature by an arbitrary factor in the degenerate regime ($T\lesssim E_F$).