Random Magnetic Impurities and the Landau Problem

Abstract

The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when $\alpha \simeq 0.3-0.4$, from an "almost free" density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail- to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analytical- are presented.

22 pages, latex, 4 figures upon request

References in corpus (6)

• Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance
• On $\delta$ perturbative interactions in the Aharonov-Bohm and Anyon Models
• Magnetic Moment and Perturbation Theory with Singular Magnetic Fields
• Three-Loop Calculation of the Anyonic Full Cluster Expansion
• Persistent Current of Free Electrons in the Plane
• Scattering From a Two Dimensional Array of Flux Tubes: A Study of The Validity of Mean Field Theory

Cited by in corpus (20)

• Functionals of the Brownian motion, localization and metric graphs
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Area distribution of two-dimensional random walks on a square lattice
• Paraxial propagation of a quantum charge in a random magnetic field
• Hall Conductivity for Two Dimensional Magnetic Systems
• Aharonov-Bohm effect on the Poincaré disk
• Persistent Currents and Magnetization in two-dimensional Magnetic Quantum Systems
• Non-Abelian Chern-Simons Particles in an External Magnetic Field
• Quantum Mechanics of a Particle with Two Magnetic Impurities
• Random Aharonov-Bohm vortices and some funny families of integrals
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Zero modes in a system of Aharonov--Bohm solenoids on the Lobachevsky plane
• Aharonov-Bohm effect with many vortices
• Scattering on two Aharonov-Bohm vortices with opposite fluxes
• Density Correlations of Magnetic Impurities and Disorder
• Algebraic and arithmetic area for $m$ planar Brownian paths
• Numerical studies of planar closed random walks
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• Random Aharonov-Bohm vortices and some exact families of integrals: Part II