Localization of electronic states in amorphous materials: recursive Green's function method and the metal-insulator transition at E<>0

TL;DR

This study uses a recursive Green's function method to numerically analyze the metal-insulator transition in amorphous materials, focusing on the critical behavior and mobility edge outside the band center.

Contribution

It provides a numerical verification of scaling assumptions and determines the critical exponent and mobility edge at energies outside the band center.

Findings

Conductivity follows a power law near the critical energy.

Critical exponent and mobility edge are numerically determined.

Scaling assumptions are confirmed for energies outside the band center.

Abstract

In this paper we will investigate whether the scaling assumptions made in previous studies for the transition at energies outside the band centre can be reconfirmed in numerical calculations, and in particular whether the conductivity sigma follows a power law close to the critical energy E_c. For this purpose we will use the recursive Green's function method to calculate the four-terminal conductance of a disordered system for fixed disorder strength at temperature T=0. Applying the finite-size scaling analysis we will compute the critical exponent and determine the mobility edge, i.e. the MIT outside the band centre.