Quantum dots: a doorway to nanoscale physics

183 Pages·2005·3.469 MB·English

by  R. Shankar (auth.), W. Dieter Heiss (eds.)

Lecture Notes in Physics
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W. Dieter Heiss (Ed.)
Quantum Dots:
a Doorway
to Nanoscale Physics
123
Editor
W.DieterHeiss
UniversityofStellenbosch
DepartmentofPhysics
MATIELAND7602
SouthAfrica
W.DieterHeiss (Ed.),QuantumDots:aDoorwaytoNanoscalePhysics,
Lect.NotesPhys.667(Springer,BerlinHeidelberg2005),DOI10.1007/b103740
LibraryofCongressControlNumber:2005921338
ISSN0075-8450
ISBN3-540-24236-8SpringerBerlinHeidelbergNewYork
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Preface
Nanoscale physics, nowadays one of the most topical research subjects, has
two major areas of focus. One is the important field of potential applications
bearing the promise of a great variety of materials having specific properties
that are desirable in daily life. Even more fascinating to the researcher in
physicsarethefundamentalaspectswherequantummechanicsisseenatwork;
mostmacroscopicphenomenaofnanoscalephysicscanonlybeunderstoodand
described using quantum mechanics. The emphasis of the present volume is
on this latter aspect.
It fits perfectly within the tradition of the South African Summer Schools
in Theoretical Physics and the fifteenth Chris Engelbrecht School was de-
voted to this highly topical subject. This volume presents the contents of
lecturesfromfourspeakersworkingattheforefrontofnanoscalephysics.The
first contribution addresses some more general theoretical considerations on
Fermi liquids in general and quantum dots in particular. The next topic is
moreexperimentalinnatureanddealswithspintronicsinquantumdots.The
alertreaderwillnoticetheclosecorrespondencetotheSouthAfricanSummer
Schoolin2001,publishedinLNP587.Thefollowingtwosectionsaretheoreti-
caltreatmentsoflowtemperaturetransportphenomenaandelectronscatter-
ingonnormal-superconductinginterfaces(Andreevbilliards).Theenthusiasm
and congenial atmosphere created by the speakers will be remembered well
byallparticipants.ThebeautifulsceneryoftheDrakensbergsurroundingthe
venue contributed to the pleasant spirit prevailing during the school.
AconsiderablecontingentofparticipantscamefromAfricancountriesout-
side South Africa and were supported by a generous grant from the Ford
Foundation; the organisers gratefully acknowledge this assistance.
The Organising Committee is indebted to the National Research Founda-
tion for its financial support, without which such high level courses would be
impossible.WealsowishtoexpressourthankstotheeditorsofLectureNotes
inPhysicsandSpringerfortheirassistanceinthepreparationofthisvolume.
Stellenbosch WD Heiss
February 2005

List of Contributors
R. Shankar NTT Basic Research Laboratories,
Sloane Physics Lab, Yale University, Atsugi-shi, Kanagawa 243-0129,
New Haven CT 06520 Japan
[email protected]
L.M.K. Vandersypen
J.M. Elzerman Kavli Institute of Nanoscience Delft,
Kavli Institute of Nanoscience Delft, PO Box 5046, 2600 GA Delft,
PO Box 5046, 2600 GA Delft, The Netherlands
The Netherlands
L.P. Kouwenhoven
ERATO Mesoscopic Correlation Kavli Institute of Nanoscience Delft,
Project, University of Tokyo, PO Box 5046, 2600 GA Delft,
Bunkyo-ku, Tokyo 113-0033, Japan The Netherlands
[email protected]
ERATO Mesoscopic Correlation
R. Hanson Project, University of Tokyo,
Kavli Institute of Nanoscience Delft, Bunkyo-ku, Tokyo 113-0033, Japan
PO Box 5046, 2600 GA Delft,
M. Pustilnik
The Netherlands
School of Physics, Georgia Institute
of Technology,
L.H.W. van Beveren
Atlanta, GA 30332, USA
Kavli Institute of Nanoscience Delft,
PO Box 5046, 2600 GA Delft, L.I. Glazman
The Netherlands William I. Fine Theoretical
ERATO Mesoscopic Correlation Physics Institute,
Project, University of Tokyo, University of Minnesota,
Bunkyo-ku, Tokyo 113-0033, Japan Minneapolis, MN 55455, USA
S. Tarucha C.W.J. Beenakker
ERATO Mesoscopic Correlation Instituut-Lorentz,
Project, University of Tokyo, Universiteit Leiden,
Bunkyo-ku, Tokyo 113-0033, P.O. Box 9506, 2300 RA Leiden,
Japan The Netherlands

Contents
A Guide for the Reader ....................................... 1
The Renormalization Group Approach – From Fermi Liquids
to Quantum Dots
R. Shankar...................................................... 3
1 The RG: What, Why and How................................. 3
2 The Problem of Interacting Fermions ........................... 4
3 Large-N Approach to Fermi Liquids ............................ 10
4 Quantum Dots............................................... 12
References ...................................................... 23
Semiconductor Few-Electron Quantum Dots
as Spin Qubits
J.M. Elzerman, R. Hanson, L.H.W. van Beveren, S. Tarucha,
L.M.K. Vandersypen, and L.P. Kouwenhoven ....................... 25
1 Introduction ................................................. 26
2 Few-Electron Quantum Dot Circuit
with Integrated Charge Read-Out .............................. 47
3 Excited-State Spectroscopy on a Nearly Closed Quantum Dot
via Charge Detection ......................................... 58
4 Real-Time Detection of Single Electron Tunnelling
using a Quantum Point Contact................................ 66
5 Single-Shot Read-Out of an Individual Electron Spin
in a Quantum Dot............................................ 72
6 Semiconductor Few-Electron Quantum Dots
as Spin Qubits ............................................... 82
References ...................................................... 92
Low-Temperature Conduction of a Quantum Dot
M. Pustilnik and L.I. Glazman .................................... 97
1 Introduction ................................................. 97
2 Model of a Lateral Quantum Dot System........................ 99
X Contents
3 Thermally-Activated Conduction ...............................105
4 Activationless Transport
through a Blockaded Quantum Dot.............................109
5 Kondo Regime in Transport through a Quantum Dot .............113
6 Discussion...................................................124
7 Summary....................................................126
References ......................................................127
Andreev Billiards
C.W.J. Beenakker................................................131
1 Introduction .................................................131
2 Andreev Reflection ...........................................134
3 Minigap in NS Junctions ......................................135
4 Scattering Formulation........................................137
5 Stroboscopic Model...........................................139
6 Random-Matrix Theory .......................................141
7 Quasiclassical Theory .........................................156
8 Quantum-To-Classical Crossover ...............................162
9 Conclusion ..................................................169
A Excitation Gap in Effective RMT and Relationship
with Delay Times ............................................170
References ......................................................172