%A A. I. Arbab
%T The quantum Hall's effect: A quantum electrodynamic phenomenon
%0 Journal Article
%D 2012
%J Chin. Phys. B
%R 10.1088/1674-1056/21/12/127301
%P 127301-127301
%V 21
%N 12
%U {http://cpb.iphy.ac.cn/CN/abstract/article_50989.shtml}
%8 2012-11-01
%X 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}=2*πh*^{2}*n*_{s}/*em*, where *n*_{s} is the electron number density, for a 2-dimensional system, and *h*=2*πh* 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}=2*πm*/*e*^{2}*n*_{s} and *C*_{H}=*me*^{2}/2*πh*^{2}*n*_{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.