| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Prev
Next
|
|
|
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 |
|
|
|
|
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, VH=2πh2ns/em, where ns 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 LH=2πm/e2ns and CH=me2/2πh2ns satisfying resonance condition with resonant frequency equals 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 propagates in the 2-dimensional gas.
|
Received: 23 May 2012
Revised: 28 June 2012
Accepted manuscript online:
|
|
PACS:
|
73.40.Hm-
|
|
| |
72.20.My
|
(Galvanomagnetic and other magnetotransport effects)
|
| |
41.20.-q
|
(Applied classical electromagnetism)
|
|
Corresponding Authors:
A. I. Arbab
E-mail: aiarbab@uofk.edu
|
Cite this article:
A. I. Arbab The quantum Hall's effect: A quantum electrodynamic phenomenon 2012 Chin. Phys. B 21 127301
|
| [1] |
Hall E 1879 Am. J. Math. 11 287
|
| [2] |
von Klitzing, K, Dorda, G and Pepper M 1980 Phys. Rev. Lett. 45 494
|
| [3] |
Laughlin R B 1983 Phys. Rev. Lett. 50 1395
|
| [4] |
Tsui D C, Stormer H L and Gossard A C 1982 Phys. Rev. Lett. 48 1559
|
| [5] |
Arbab A I 2012 Europhys. Lett. 98 30008
|
| [6] |
Arbab A I http://arxiv.org/abs/1203.0613
|
| [7] |
Cage M E and Jeffery A 1996 J. Res. Natl. Inst. Stand. Technol. 101 733
|
| [8] |
Arbab A I 2012 Chin. Phys. Lett. 00 submitted
|
| [9] |
London F 1948 Phys. Rev. 74 562
|
| [10] |
Ashcroft N W and Mermin N D 1976 Solid State Physics (Harcourt College Pubs.) 1976
|
| [11] |
Luryi S 1988 Appl. Phys. Lett. 52 501
|
| [12] |
Bjorken J D and Drell S D 1964 Relativistic Quantum Mechanics (McGraw-Hill)
|
| [13] |
Casimir H B G 1948 Proc. K. Ned. Akad. Wet. 51 793
|
| [14] |
Devoret M H 1997 Quantum Fluctuations (Amsterdam: Elsevier Science B. V.)
|
| [15] |
Novoselov K S et al. 2005 Nature 438 197
|
| [16] |
Dirac P A M 1931 Proc. Roy. Soc. London. A 133 60
|
| [17] |
Dirac P A M 1948 Phys. Rev. 74 817
|
| [18] |
von Klitzing K 2004 Séminaire Poincaré 2 1
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
