Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect

Version 1 : Received: 4 December 2021 / Approved: 6 December 2021 / Online: 6 December 2021 (12:49:01 CET)

How to cite: Ishiguri, S. Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect. Preprints 2021, 2021120072 (doi: 10.20944/preprints202112.0072.v1). Ishiguri, S. Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect. Preprints 2021, 2021120072 (doi: 10.20944/preprints202112.0072.v1).

Abstract

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

Keywords

Integer quantum Hall effect; Fractional quantum Hall effect; stationary wave; nodes in stationary wave; quantization of electric charge; the plateau of quantized resistivity

Subject

PHYSICAL SCIENCES, Condensed Matter Physics

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