On edge states in semi-infinite quantum Hall systems

Abstract

We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total Hamiltonian necessarily has a continuous spectrum in some intervals in-between the Landau levels provided that both the amplitude and spatial variation of the impurity potential are sufficiently weak. The spatial decay of the impurity potential is not needed. In particular this proves the occurence of edge states in semi-infinite quantum Hall systems.

20 pages, no figures, plain TEX, to appear in J. Phys. A

Cited by in corpus (19)

• Simultaneous quantization of edge and bulk Hall conductivity
• Spectra of soft ring graphs
• Curvature-induced bound states in Robin waveguides and their asymptotical properties
• Persistent currents for 2D Schrödinger operator with a strong $\delta$-interaction on a loop
• Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries
• Magnetic strip waveguides
• Universality in Quantum Hall Systems: Coset Construction of Incompressible States
• Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
• Extended Edge States in Finite Hall Systems
• Magnetic transport in a straight parabolic channel
• T-duality and the bulk-boundary correspondence
• Spectral Properties of Finite Quantum Hall Systems
• Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
• Spectral flow and level spacing of edge states for quantum Hall hamiltonians
• Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice
• Persistent currents due to point obstacles
• Magnetic quantum currents in the presence of a Neumann wall
• Magnetic fields and boundary conditions in spectral and asymptotic analysis
• Magnetic transport in laterally coupled layers