The quantum Hall's effect: A quantum electrodynamic phenomenon

doi:10.1088/1674-1056/21/12/127301

Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 127301-127301.doi: 10.1088/1674-1056/21/12/127301

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇下一篇

The quantum Hall's effect: A quantum electrodynamic phenomenon

A. I. Arbab

Department of Physics, Faculty of Science, University of Khartoum, P. O. Box 321, Khartoum 11115, Sudan

收稿日期:2012-05-23 修回日期:2012-06-28 出版日期:2012-11-01 发布日期:2012-11-01

The quantum Hall's effect: A quantum electrodynamic phenomenon

A. I. Arbab

Department of Physics, Faculty of Science, University of Khartoum, P. O. Box 321, Khartoum 11115, Sudan

Received:2012-05-23 Revised:2012-06-28 Online:2012-11-01 Published:2012-11-01
Contact: A. I. Arbab E-mail:aiarbab@uofk.edu

摘要/Abstract

摘要： We have applied Maxwell's equations to study the physics of quantum Hall's effect. The electromagnetic properties of this system are obtained. The Hall's voltage, V_H=2πh²n_s/em, where n_s is the electron number density, for a 2-dimensional system, and h=2πh is the Planck's constant, is found to coincide with the voltage drop across the quantum capacitor. Consideration of the cyclotronic motion of electrons is found to give rise to Hall's resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level, the Hall's effect is found to be equivalent to a resonant LCR circuit with L_H=2πm/e²n_s and C_H=me²/2πh²n_s satisfying resonance condition with resonant frequency equals to the inverse of the scattering (relaxation) time, τ_s. The Hall's resistance is found to be R_H=√L_H/C_H. The Hall's resistance may be connected with the impedance that the electron wave experiences when propagates in the 2-dimensional gas.

关键词: quantum Hall effect, Maxwell equations, electromagnetism

Abstract: We have applied Maxwell's equations to study the physics of quantum Hall's effect. The electromagnetic properties of this system are obtained. The Hall's voltage, V_H=2πh²n_s/em, where n_s is the electron number density, for a 2-dimensional system, and h=2πh is the Planck's constant, is found to coincide with the voltage drop across the quantum capacitor. Consideration of the cyclotronic motion of electrons is found to give rise to Hall's resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level, the Hall's effect is found to be equivalent to a resonant LCR circuit with L_H=2πm/e²n_s and C_H=me²/2πh²n_s satisfying resonance condition with resonant frequency equals to the inverse of the scattering (relaxation) time, τ_s. The Hall's resistance is found to be R_H=√L_H/C_H. The Hall's resistance may be connected with the impedance that the electron wave experiences when propagates in the 2-dimensional gas.

Key words: quantum Hall effect, Maxwell equations, electromagnetism

中图分类号:

73.40.Hm-

72.20.My (Galvanomagnetic and other magnetotransport effects) 41.20.-q (Applied classical electromagnetism)

A. I. Arbab. The quantum Hall's effect: A quantum electrodynamic phenomenon[J]. Chin. Phys. B, 2012, 21(12): 127301-127301.

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The quantum Hall's effect: A quantum electrodynamic phenomenon

The quantum Hall's effect: A quantum electrodynamic phenomenon

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