Introduction to the Theory of the Integer Quantum Hall Effect

Abstract

Part 1 Introduction - Basic Facts: The Integer Quantum Hall Effect Classical Dynamics Quantizing Magnetic Fields The Eigenvalue Problem The Landau Model Models of Confinement Bloch Representation Disorder Broadening. Part 2 Quantum Hall Effect for Pedestrians - High Field Model: Confined Cylinder Model Spectral Conditions for the Quantum Hall Effect Systems with Contacts Robustness of the Quantum Hall Effect. Part 3 Linear Response Isothermal Susceptibilities: Dynamic Susceptibilities Conductivity Tensor Spectral Decomposition Conductivitie in Spectral Decomposition Hall Conductivity in Terms of the Center Coordinates - Multi-Probe Systems Conductance and Geometry Problems in Magnetotransport Calculations. Part 3 Phenomenology of Global Conductivities - Quantum Langevin Equation: Mori Theory Localization Criteria Hall Plateaus and Mobility Edges Finite Temperatures. Part 4 Localization in High Landau Bands - Quantum Corrections to the Conductivity: Quantum Wires Weak Localization Regime in the Quantum Hall Effect Localization in the Tails of High Landau Bands. Part 5 Averaging Green Functions - Gaussian Path Integrals: Supersymmetry Method Replica Tyick The Instanton Free Energy. Part 6 Localization in the Lowest Landau Band Density of States: Improved Perturbation Methods Inverse Participation Number Instanton Method - Density of States Localization in Band Tails.