Random Magnetic Impurities and the $\delta$ Impurity Problem

TL;DR

This paper investigates how random magnetic impurities affect the two-dimensional electron density of states in a magnetic field, mapping the problem to a contact delta impurity model and analyzing it via Brownian motion techniques.

Contribution

It introduces a novel mapping of the random magnetic impurity problem onto a contact delta impurity problem within the lowest Landau level and proposes a Brownian motion analysis method.

Findings

Mapping of the impurity problem to a delta impurity model

Analysis of the density of states under disorder

Application of Brownian motion techniques to the model

Abstract

One considers the effect of disorder on the 2-dimensional density of states of an electron in a constant magnetic field superposed onto a Poissonnian random distribution of point vortices. If one restricts the electron Hilbert space to the lowest Landau level of the total average magnetic field, the random magnetic impurity problem is mapped onto a contact $\delta$ impurity problem. A brownian motion analysis of the model, based on brownian probability distributions for arithmetic area winding sectors, is also proposed. PACS numbers: 05.30.-d, 05.40.+j, 11.10.-