Characterization of the Spectrum of the Landau Hamiltonian with Delta Impurities

Abstract

We consider a random Schrodinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the spectrum in the lowest N Landau bands of this random Hamiltonian when the magnetic field is sufficiently strong, depending on N. We show that the spectrum in these bands is entirely pure point, that the energies coinciding with the Landau levels are infinitely degenerate and that the eigenfunctions corresponding to energies in the remainder of the spectrum are localized with a uniformly bounded localization length. By relating the Hamiltonian to a lattice operator we are able to use the Aizenman-Molchanov method to prove localization.

To appear in Commun. Math. Phys. (1999)

Cited by in corpus (11)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Moment Analysis for Localization in Random Schroedinger Operators
• Spectral Localization by Gaussian Random Potentials in Multi-Dimensional Continuous Space
• Existence and uniqueness of the integrated density of states for Schrödinger operators with magnetic fields and unbounded random potentials
• Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries
• Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
• Extended Edge States in Finite Hall Systems
• A self-adjointness criterion for the Schrödinger operator with infinitely many point interactions and its application to random operators
• Localization on quantum graphs with random vertex couplings
• Spectral flow and level spacing of edge states for quantum Hall hamiltonians
• The Spectrum of a Magnetic Schrödinger Operator with Randomly Located Delta Impurities