Divergence of effective mass in 'Uncorrelated State Percolation' Model

TL;DR

This paper investigates whether the divergence of effective mass in 2D metal-insulator transitions aligns with percolation theory, using a model to analyze effective mass scaling near the percolation threshold.

Contribution

It demonstrates that the effective mass diverges with a specific critical exponent in a 2D percolation model, linking MIT behavior to classical percolation universality.

Findings

Effective mass scales as m*~(P-Pc)^a with a=1

Divergence occurs at the classical percolation threshold

Supports universality class similarity between MIT and percolation

Abstract

We want to answer the question of whether the divergence in the effective mass in metal-insulator transition (MIT) in 2DEG is in the same universality class as percolation. We use a model to make Percolated state in 2D and then calculate the effective mass in a super-cell and the Bloch Theorem. It is seen that the effective mass, m*, scales as m*~(P-Pc)^a with a=1 and Pc being the (classical) percolation threshold.