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Dieter Heiss (Ed.) Quantum Dots: a Doorway to Nanoscale Physics 123 www. Dieter Heiss University of Stellenbosch Department of Physics MATIELAND 7602 South Africa W. Dieter Heiss (Ed.), Quantum Dots: a Doorway to Nanoscale Physics, Lect.1007/b103740 Library of Congress Control Number: 2005921338 ISSN 0075-8450 ISBN 3-540-24236-8 Springer Berlin Heidelberg New York 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, reuse of illustra- tions, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks.
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Typesetting: Camera-ready by the authors/editor Data conversion by TechBooks Cover design: design & production, Heidelberg Printed on acid-free paper 54/3141/jl - 5 4 3 2 1 0 www.com 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 physics are the fundamental aspects where quantum mechanics is seen at work; most macroscopic phenomena of nanoscale physics can only be understood and 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 lectures from four speakers working at the forefront of nanoscale physics. The first contribution addresses some more general theoretical considerations on Fermi liquids in general and quantum dots in particular. The next topic is more experimental in nature and deals with spintronics in quantum dots.
The alert reader will notice the close correspondence to the South African Summer School in 2001, published in LNP 587. The following two sections are theoreti- cal treatments of low temperature transport phenomena and electron scatter- ing on normal-superconducting interfaces (Andreev billiards). The enthusiasm and congenial atmosphere created by the speakers will be remembered well by all participants. The beautiful scenery of the Drakensberg surrounding the venue contributed to the pleasant spirit prevailing during the school.
A considerable contingent of participants came from African countries out- 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. We also wish to express our thanks to the editors of Lecture Notes in Physics and Springer for their assistance in the preparation of this volume. Stellenbosch WD Heiss February 2005 www.com List of Contributors R.
Shankar NTT Basic Research Laboratories, Sloane Physics Lab, Yale University, Atsugi-shi, Kanagawa 243-0129, New Haven CT 06520 Japan r. 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. 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 elzerman@qt.nl 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 L. van Beveren of Technology, Kavli Institute of Nanoscience Delft, Atlanta, GA 30332, USA PO Box 5046, 2600 GA Delft, L. 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.
Beenakker ERATO Mesoscopic Correlation Instituut-Lorentz, Project, University of Tokyo, Universiteit Leiden, Bunkyo-ku, Tokyo 113-0033, P. Box 9506, 2300 RA Leiden, Japan The Netherlands www.com Contents A Guide for the Reader. 1 The Renormalization Group Approach – From Fermi Liquids to Quantum Dots R. 3 1 The RG: What, Why and How.
3 2 The Problem of Interacting Fermions. 4 3 Large-N Approach to Fermi Liquids. 23 Semiconductor Few-Electron Quantum Dots as Spin Qubits J. 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.
92 Low-Temperature Conduction of a Quantum Dot M. 97 2 Model of a Lateral Quantum Dot System .com 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.
131 2 Andreev Reflection. 134 3 Minigap in NS Junctions. 139 6 Random-Matrix Theory. 156 8 Quantum-To-Classical Crossover.
169 A Excitation Gap in Effective RMT and Relationship with Delay Times .com A Guide for the Reader Quantum dots, often denoted artificial atoms, are the exquisite tools by which quantum behavior can be probed on a scale appreciably larger than the atomic scale, that is, on the nanometer scale. In this way, the physics of the devices is closer to classical physics than that of atomic physics but they are still sufficiently small to clearly exhibit quantum phenomena. The present volume is devoted to some of these fascinating aspects. In the first contribution general theoretical aspects of Fermi liquids are addressed, in particular, the renormalization group approach.
The choice of appropriate variables as a result of averaging over “unimportant” variables is presented. This is then aptly applied to large quantum dots. The all impor- tant scales, ballistic dots and chaotic motion are discussed. Nonperturbative methods and critical phenomena feature in this thorough treatise.
The tra- ditional phenomenological Landau parameters are given a more satisfactory theoretical underpinning. A completely different approach is encountered in the second contribution in that it is a thorough experimental expose of what can be done or expected in the study of small quantum dots. Here the emphasis lies on the electron spin to be used as a qubit. The experimental steps toward using a single electron spin – trapped in a semiconductor quantum dot – as a spin qubit are described.
The introduction contains a resume of quantum computing with quantum dots. The following sections address experimental implementations, the use of different quantum dot architectures, measurements, noise, sensitivity and high-speed performance. The lectures are based on a collaborative effort of research groups in the Netherlands and in Japan. The last two contributions are again theoretical in nature and address particular aspects relating to quantum dots.
In the third lecture series, mech- anisms of low-temperature electronic transport through a quantum dot – weakly coupled to two conducting leads – are reviewed. In this case transport is dominated by electron–electron interaction. At moderately low temperatures (comparing with the charging energy) the linear conductance is suppressed by www.com 2 A Guide for the Reader the Coulomb blockade. A further lowering of the temperature leads into the Kondo regime.
The fourth series of lectures deals with a very specific and cute aspect of nanophysics: a peculiar property of superconducting mirrors as discovered by Andreev about forty years ago. The Andreev reflection at a superconductor modifies the excitation spectrum of a quantum dot. The difference between a chaotic and integrable billiard (quantum dot) is discussed and relevant clas- sical versus quantum time scales are given. The results are a challenge to experimental physicists as they are not confirmed as yet.com The Renormalization Group Approach – From Fermi Liquids to Quantum Dots R.
Shankar Sloane Physics Lab, Yale University, New Haven CT 06520 r.