Geometric Properties of Transport in Quantum Hall Systems
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In this first section, we present a short review of theoretical approaches to the quantum Hall effect. For an in depth coverage, we refer to the recent book D. J. Thouless (1998), as well as to M. Stone (1992). Let us recall how a quantum Hall system in a laboratory looks like: a strong magnetic field runs perpendicular through a probe of a conductor or semiconductor, forming a two-dimensional system; this setup is typically realized as inversion layers in field effect transistors, formed at the interface between an insolator and a semiconductor under the influence of an electric field perpendicular to the interface. If the temperature of the system is near zero, the electrons are bo- und by a deep potential well, forming a two-dimensional system. We identify this inversion layer with the x-y plane, hence B is parallel to the z-axis.
KeywordsGeometric Property Edge State Hall Conductance Chern Character Adiabatic Limit
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