The quantum Hall's effect:A quantum electrodynamic phenomenon

作     者：A.I.Arbab 

作者机构：Department of PhysicsFaculty of ScienceUniversity of Khartoum 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2012年第21卷第12期

页      面：444-450页

核心收录：

学科分类：0710[理学-生物学] 07[理学] 070201[理学-理论物理] 071002[理学-动物学] 0702[理学-物理学] 

基　　金：Sultan Qaboos University (Oman) for the visiting grant 

主　　题：quantum Hall effect Maxwell equations electromagnetism 

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, VH ---- 27rh2ns/em, where ns is the electron number density, for a 2- dimensional system, and h ---- 27rh 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 LH = 2π m/e2ns and CH -= me2/π2h2ns satisfying the resonance condition with resonant frequency equal to the inverse of the scattering （relaxation） time, τs. The Hall＇s resistance is found to be RH = √LH/CH The Hall＇s resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas.