Abstract
We discuss a model of both the classical and the integer quantum Hall effect which is based on a semiclassical Schrödinger-Chern-Simons action, where the Ohm equations result as equations of motion. The quantization of the classical Chern-Simons part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall effect is described by a theory which arises as the classical limit of a theory of the quantum Hall effect. The model also explains the preference and the domain of the edge currents on the boundary of samples.
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Ghaboussi, F. Quantum theory of the Hall effect. Int J Theor Phys 36, 923–934 (1997). https://doi.org/10.1007/BF02435792
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DOI: https://doi.org/10.1007/BF02435792