Quantized Hall effect and edge currents

Abstract

It is shown that the quantized Hall current may always be expressed as the difference between diamagnetic currents flowing at the two edges. It is argued that the high precision of the quantization may be aided by the establishment of a local equilibrium in each edge region. The basic ideas are illustrated by the discussion of a free two-dimensional electron gas in an infinite confining potential. Our derivation establishes the connection between quantum-mechanical and classical thermodynamic explanations for the quantum Hall effect.