Introduction to the Theory of the Integer Quantum Hall Effect
Published on 9. August 1994
Book
Paperback/Softback
VIII, 296 pages
978-3-527-29209-7 (ISBN)
Description
The quantum hall effect (QHE) is an important topic for those studying the way electrons move in materials, particularly in structures that confine such a movement in one or more dimensions (low-dimensional structures). This book provides an introduction to the ways of using the various models that try to explain diverse aspects of the QHE, an effect that is still not properly understood. Some chapters, such as "critical phenomena" and "multifractal analysis" should be of interest to a wider audience than those studying QHE.
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Content
Introduction Basic Facts The Integer Quantum Hall Effect.................................. ClassicalDynamics . . . . . . . . . . . . Quantizing Magnetic Fields....................................... The Eigenvalue Problem........................................... The Landau Model . . . . . . . . Models of Confinement.................................. Bloch Representation............................................. Disorder Broadening.............................................. Summary......................................................... . Guide for Further Reading........................................ 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........................ Summary . . . . . . . Guide for Further Reading.................................... 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................. Summary......................................................... . ... Guide for Purther Reading . . . . . . . . . . . . . Phenomenology of Global Conductivities Quantum Langevin Equation............... Mori Theory....................... Localization Criteria............................................... Hall Plateaus and Mobility Edges............................... Finite Temperatures.................. Summary . . . . . . . . . . GuideforFurtherReading........................ 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............ Summary . . . . . . . . . . . . . . Guide for Further Reading . . . . . . Averaging Green Functions Gaussian Path Integrals . . . . . . . . . Supersymmetry Method......................................... Replica Tyick........................................................ The Instanton Free Energy . . . . . . . . . . . . . . Summary . . . . . . . . . . . . Guide for Further Reading............................... Localization in the Lowest Landau Band Density of States........ Improved Perturbation Methods... Inverse Paxticipation Number.... Instanton Method - Density of States........................ Localization in Band Tails........................................