The Quantum Hall Effect: Poincaré Seminar 2004

206 Pages·2005·3.866 MB·English

by  Benoît Douçot, Vincent Pasquier, Vincent Rivasseau

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Progress in Mathematical Physics
Volume 45
Editors-in-Chief
Anne Boutet de Monvel,Université Paris VII Denis Diderot,France
Gerald Kaiser,Center for Signals and Waves,Austin,TX,USA
Editorial Board
Sir M.Berry,University of Bristol, UK
C.Berenstein,University of Maryland,College Park,USA
P.Blanchard,University of Bielefeld, Germany
A.S.Fokas,University of Cambridge, UK
D.Sternheimer,Université de Bourgogne, Dijon, France
C.Tracy,University of California,Davis,USA
PMP_7300_Doucot_Titelei 15.6.2005 15:58 Uhr Seite 3
The Quantum Hall Effect
Poincaré Seminar 2004
Benoît Douçot
Bertrand Duplantier
Vincent Pasquier
Vincent Rivasseau
Editors
Birkhäuser Verlag
Basel Boston Berlin
• •
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Editors:
Benoît Douçot Bertrand Duplantier
LPTHE Service de Physique Théorique
CNRS et Universités Paris 6 et 7 Orme des Merisiers
Tour 24-14 5e étage CEA –Saclay
4 place Jussieu F-91191 Gif-sur-Yvette Cedex
F-75252 Paris Cedex 05 e-mail:[email protected]
e-mail:[email protected]
Vincent Pasquier Vincent Rivasseau
Service de Physique Théorique Laboratoire de Physique Théorique
Orme des Merisiers Université Paris XI
CEA –Saclay F-91405 Orsay Cedex
F-91191 Gif sur Yvette Cedex e-mail:[email protected]
e-mail:[email protected]
2000 Mathematics Subject Classification 81V70
A CIP catalogue record for this book is available from the Library of Congress,Washington D.C.,
USA
Bibliographic information published by Die Deutsche Bibliothek
Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie;
detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>.
ISBN 3-7643-7300-8 Birkhäuser Verlag,Basel – Boston – Berlin
This work is subject to copyright.All rights are reserved,whether the whole or part of the material
is concerned,specifically the rights of translation,reprinting,re-use of illustrations,broadcasting,
reproduction on microfilms or in other ways,and storage in data banks.For any kind of use
whatsoever,permission from the copyright owner must be obtained.
© 2005 Birkhäuser Verlag,P.O.Box 133,CH-4010 Basel,Switzerland
Part of Springer Science+Business Media
Printed on acid-free paper produced of chlorine-free pulp.TCF (cid:39)
Printed in Germany
ISBN-10:3-7643-7300-8
ISBN-13:978-3-7643-7300-9
9 8 7 6 5 4 3 2 1 www.birkhauser.ch
Contents
Foreword.....................................................................vii
Klaus von Klitzing
25 Years of Quantum Hall Effect (QHE)
A Personal View on the Discovery, Physics and Applications
of this Quantum Effect...................................................1
Benoˆıt Douc¸ot and Vincent Pasquier
Physics in a Strong Magnetic Field......................................23
Beat Jeckelmann and Blaise Jeanneret
The Quantum Hall Effect as an Electrical Resistance Standard...........55
Steven M. Girvin
Introduction to the Fractional Quantum Hall Effect.....................133
D. Christian Glattli
Tunneling Experiments in
the Fractional Quantum Hall Effect Regime.............................163
We thank the Institute of Physics Publishing for its authorizationto repro-
duce the paper by B. Jeckelmann and B. Jeanneret.

Foreword
This book is the third in a series of lectures of the S´eminaire Poincar´e, which is
directed towards a large audience of physicists and of mathematicians.
The goal of this seminar is to provide up to date information about general
topics of great interest in physics. Both the theoretical and experimental aspects
are covered, with some historical background. Inspired by the Bourbaki seminar
in mathematics in its organization, hence nicknamed “Bourbaphi”, this Poincar´e
SeminarisheldtwiceayearattheInstitutHenriPoincar´einParis,withcontribu-
tions prepared in advance. A particular care is devoted to the pedagogicalnature
ofthe presentationsoas tofulfill the goalofbeing readablebya largeaudience of
scientists.
ThisvolumecontainsthesixthsuchSeminar,heldin2004.Itisdevotedtothe
Quantum Hall Effect. After a historical and general presentation by Nobel prize
Klaus von Klitzing, discovererof this effect, the volume proceeds with reviews on
the mathematics and physics of both the integer and fractionalcase,and includes
up to date presentations of the tunneling and metrology experiments related to
the Quantum Hall Effect.
Wehopethatthepublicationofthisserieswillservethecommunityofphysi-
cists and mathematicians at professional or graduate student level.
We thank the Commissariat `a l’E´nergie Atomique (Division des Sciences de
laMati`ere),theCentreNationaldelaRechercheScientifique(SciencesPhysiqueet
Math´ematiques), and the Daniel Iagolnitzer Foundation for sponsoring the Semi-
nar. Special thanks are due to Chantal Delongeas for the preparationof the man-
uscript.
Benoˆıt Douc¸ot
Bertrand Duplantier
Vincent Pasquier
Vincent Rivasseau

TheQuantumHallEffect,1–21
(cid:1)c Birkh¨auserVerlag,Basel,2005 Poincar´e Seminar 2004
25 Years of Quantum Hall Effect (QHE)
A Personal View on the Discovery,
Physics and Applications of this Quantum Effect
Klaus von Klitzing
1 Historical Aspects
The birthday of the quantum Hall effect (QHE) can be fixed very accurately. It
was the night of the 4th to the 5th of February 1980 at around 2 a.m. during
an experiment at the High Magnetic Field Laboratory in Grenoble. The research
topicincludedthecharacterizationoftheelectronictransportofsiliconfieldeffect
transistors. How can one improve the mobility of these devices? Which scattering
processes (surface roughness, interface charges, impurities etc.) dominate the mo-
tionoftheelectronsintheverythinlayerofonlyafewnanometersattheinterface
betweensiliconandsilicondioxide?Forthisresearch,Dr.Dorda(SiemensAG)and
Dr. Pepper (Plessey Company) provided specially designed devices (Hall devices)
as shown in Fig.1, which allow direct measurements of the resistivity tensor.
For the experiments, low temperatures (typically 4.2 K) were used in order
to suppress disturbing scattering processes originating from electron-phonon in-
teractions. The application of a strong magnetic field was an established method
toget more informationabout microscopic details of the semiconductor. A review
articlepublishedin1982byT.Ando,A.Fowler,andF.Sternabouttheelectronic
properties of two-dimensional systems summarizes nicely the knowledge in this
field at the time of the discovery of the QHE [1].
Since 1966 it was known, that electrons, accumulated at the surface of a
silicon single crystal by a positive voltage at the gate (= metal plate parallel to
the surface), form a two-dimensional electron gas [2]. The energy of the electrons
for a motion perpendicular to the surface is quantized (“particle in a box”) and
even the free motion of the electrons in the plane of the two-dimensional system
becomes quantized (Landau quantization), if a strong magnetic field is applied
perpendicular to the plane. In the ideal case, the energy spectrum of a 2DEG in
strong magnetic fields consists of discrete energy levels (normally broadened due
to impurities) with energy gaps between these levels. The quantum Hall effect is
observed, if the Fermi energy is located in the gap of the electronic spectrum and
if the temperature is so low, that excitations across the gap are not possible.
The experimental curve, which led to the discovery of the QHE, is shown in
Fig. 2. The blue curve is the electrical resistance of the silicon field effect tran-