Averaged Green function and density of states for electrons in a high magnetic field and random potential

TL;DR

This paper develops a computational method to calculate the averaged Green function and density of states for 2D electrons in a strong magnetic field with random potential, using perturbation expansion up to 12th order.

Contribution

It introduces a computer algebra program that automates the perturbation expansion for the density of states in a high magnetic field with random impurities, enabling high-order calculations.

Findings

Perturbation expansion computed up to 12th order.

Automated evaluation for Gaussian impurity potentials.

Enhanced reconstruction of the density of states.

Abstract

We consider a model for 2D electrons in a very strong magnetic field (i.e. projected onto a single Landau level) and a random potential $V$. The computation of the averaged Green function for this system reduces to calculating the averaged density of states. We have constructed a computer algebra program which automatically generates a perturbation expansion in $V$ for these quantities. This is equivalent to computing moments of the density of states. When $V$ is a sum of Gaussians from Poisson distributed impurities, each term in the perturbation expansion can be evaluated automatically. We have done so up to 12th order. The resulting information can be used to reconstruct the density of states to good precision.