Hall Conductivity in the presence of repulsive magnetic impurities

TL;DR

This paper investigates the Hall conductivity in disordered magnetic systems with repulsive impurities, revealing behaviors similar to experimental observations and discussing the effects of disorder and Landau level restrictions.

Contribution

It introduces a model of disordered magnetic systems with point vortices and analyzes the impact of disorder on Hall conductivity, connecting theoretical results with experimental findings.

Findings

Hall conductivity exhibits behavior similar to experiments with repulsive scatterers

Disordered magnetic systems with point vortices show specific conductivity patterns

Restricting to a Landau level leads to vanishing Hall conductivity

Abstract

The Hall conductivity of disordered magnetic systems consisting of hard-core point vortices randomly dropped on the plane with a Poissonian distribution, has a behavior analogous to the one observed experimentally by R.~J.~Haug, R.~R.~Gerhardts, K.~v.~Klitzling and K.~Ploog, with repulsive scatterers \cite {1}. We also argue that models of homogeneous magnetic field with disordered potential, have necessarily vanishing Hall conductivities when their Hilbert space is restricted to a given Landau level subspace.