EDGE CURRENTS FOR QUANTUM HALL SYSTEMS I: ONE-EDGE, UNBOUNDED GEOMETRIES

DOI10.1142/S0129055X08003262zbMath1145.81053arXivmath-ph/0702092OpenAlexW1979450312MaRDI QIDQ3521554

Eric Soccorsi, Peter D. Hislop

Publication date: 26 August 2008

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0702092

zbMATH Keywords

perturbation theoryspectral theoryquantum Hall effectedge statesasymptotic velocityLandau Hamiltonians

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Many-body theory; quantum Hall effect (81V70)

Related Items (12)

Limiting absorption principle for the magnetic Dirichlet Laplacian in a half-plane ⋮ Magnetic quantum currents in the presence of a Neumann wall ⋮ Non-homogeneous magnetic permeability and magnetic steps within the Ginzburg-Landau model ⋮ Edge states induced by Iwatsuka Hamiltonians with positive magnetic fields ⋮ On a quantum Hamiltonian in a unitary magnetic field with axisymmetric potential ⋮ The distribution of superconductivity near a magnetic barrier ⋮ A geometric Iwatsuka type effect in quantum layers ⋮ Discrete spectrum of quantum Hall effect Hamiltonians. I: Monotone edge potentials ⋮ Characterization of bulk states in one-edge quantum Hall systems ⋮ On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current ⋮ The bulk-edge correspondence for continuous dislocated systems ⋮ Absolutely continuous edge spectrum of Hall insulators on the lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Scattering of magnetic edge states
• The quantum Hall effect for electrons in a random potential
• Microlocalization, percolation, and Anderson localization for the magnetic Schrödinger operator with a random potential
• Edge currents in the absence of edges
• On the extended nature of edge states of quantum Hall Hamiltonians
• Boundary maps for \(C^*\)-crossed products with \(\mathbb R\) with an application to the quantum Hall effect
• Edge and impurity effects on quantization of Hall currents
• Characterization of the spectrum of the Landau Hamiltonian with delta impurities
• Equality of bulk and edge Hall conductance revisited
• Quantization of edge currents for continuous magnetic operators
• Landau Hamiltonians with random potentials: Localization and the density of states
• Equality of the bulk and edge Hall conductances in a mobility gap
• On edge states in semi-infinite quantum Hall systems
• The noncommutative geometry of the quantum Hall effect
• EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
• Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems
• Simultaneous quantization of edge and bulk Hall conductivity
• Magnetic transport in a straight parabolic channel
• Extended edge states in finite Hall systems
• On the Quantization of Hall Currents in Presence of Disorder

This page was built for publication: EDGE CURRENTS FOR QUANTUM HALL SYSTEMS I: ONE-EDGE, UNBOUNDED GEOMETRIES