Edge Current in the Quantum Hall Effect

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Abstract
A field-theoretic description of a quantum Hall system with edges is presented with emphasis on the distinction between the Hall current and the diamagnetic edge current. An edge-current picture of the quantum Hall effect is obtained, in which the edge Hall current is characterized as the Hall current expelled from the localization-dominated bulk rather than the diamagnetic current. A general argument is given to show that localization, gauge invariance, and insensitivity of the Hall current to intersubband scattering are essential for the occurrence and exactness of the quantized Hall conductance.