Single Charge Tunneling: Coulomb Blockade Phenomena In Nanostructures PDF
Preview Single Charge Tunneling: Coulomb Blockade Phenomena In Nanostructures
Nato Science Series B: {closed) Hermann Grabert Michel H. Devoret Editors Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures Single Charge Tunneling Coulomb Blockade Phenomena ln Nanostructures NATO ASI Series Advanced Science InstitutesSeries A series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientitic Affairs Division A Life Seiences Plenum Publishing Corporation B Physics New York and London C Mathematical and Physical Seiences Kluwer Academic Publishers D Behavioral and Social Seiences Dordrecht, Boston, and London E Applied Seiences F Computer and Systems Seiences Springer-Verlag G Ecological Seiences Berlin, Heidelberg, New York, London, H Cell Biology Paris, Tokyo, Hong Kong, and Barcelona I Global Environmental Change Recent Volumes in this Series Volume 287-Coherence Phenomena in Atomsand Molecules in Laser Fields edited by Andre D. Bandrauk and Stephen C. 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Devoret Centre d'Etudes de Saclay Gif-sur-Yvette, France This limited facsimile edition has been issued for the purpese of keeping this title available to the scientific community. Springer Science+Business Media, LLC Proceedings of a NATO Advanced Study Institute on Single Charge Tunneling, held March 5-15, 1991, in Les Houches, France NATo-PCo-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with key words and/or abstracts) to more than 30,000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCQ-DATA BASE is possible in two ways: -via online FILE 128 (NATO-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, ltaly. -via CD-ROM "NATO-PCO-DATA BASE" with user-friendly retrieval softwarein English, French, and German (©WTVGmbH andDATAWARETechnologies,lnc. 1989) The CD-ROM can be erdered through any member of the Board of Publishers er through NATO PCO, Overijse, Belgium. 10 9 8 7 6 5 Library of Congress Cataloging in Publication Data Single charge tunneling: Coulomb blockade phenomena in nanostructures I edited by Hermann Grabert and Michel H. Devoret. p. cm.-(NATO ASI series. Series B, Physics; v. 294} "Proceedings of a NATO Advanced Study Institute on Single Charge Tunnel ing, held March 5-15, 1991, in Les Houches, France"-Verso t.p. "Published in cooperation with NATO Scientific Affairs Division." lncludes bibliographical references and index. 1. Tunneling (Physics}-Congresses. 2. Coulomb potentiai-Congresses. 3. Nanostructures-Congresses. I. Grabert, Hermann, date. II. Devoret, Michel H. 111. NATO Advanced Study Institute on Single Charge Tunneling (1991: Les Houches, Haute-Savoie, France) IV. North Atlantic Treaty Organization. Scien tific Affairs Division. V. Series. QC176.8.T8S56 1992 92-13436 530.4'16-dc20 CIP ISBN 978-1-4757-2168-3 ISBN 978-1-4757-2166-9 (eBook) DOI 10.1007/978-1-4757-2166-9 © Springer Science+Business Media New York 1992 Origina11y published by Plenum Press, New York in 1992 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface The field of single charge tunneling comprises of phenomena where the tunneling of a microscopic charge, usually carried by an electron or a Cooper pair, leads to macro scopically observable effects. The first conference entirely devoted to this new field was the NATO Advanced Study Institute on Single Charge Tunneling held in Les Hauches, France, March 5-15, 1991. This book contains a series of tutorial articles based on lectures presented at the meeting. It was intended to provide both an introduction for nonexperts and a valuable reference summarizing the state of the art of single charge tun neling. A complementary publication with contributions by participants of the NATO Advanced Study Institute is the Special Issue on Single Charge Tunneling of Zeitschrift für Physik B, Vol. 85, pp. 317-468 (1991 ). That issue with original papers provides a snapshot af the leading edge of current research in the field. The success of the meeting and the publicatian of this volume was made possible through the generaus support af the NATO Scientific A:ffairs Division, Brussels, Belgium. The Centre de Physique des Hauches has provided a superbly situated conference site and took care af many lacal arrangements. Both far the preparation of the conference and the handling af some manuscripts the suppart af the Centre d 'Etudes de Saclay was essential. The editing of the proceedings volume would not have been passible without the dedicated efforts of Dr. G.-1. Ingald, who tailared a 1\.TEX style-file to the needs af this book, and the assistance of J. Ankerhold and P. Wyrowski from the sta:ff of the Fachbereich Physik of the Universität Essen, who prepared the manuscripts in camera ready form. The editors are most appreciative of the efforts made by the colleagues who accepted the burden of writing a chapter covering a specific aspect of single charge as tunneling in this volume, and they thank all participants of the conference well as the supporting staff for their help in making the Advanced Study Institute so successful. Michel H. Devoret Hermann Grabert Graupe Quantronique Fachbereich Physik Centre d 'Etudes de Saclay Universität Essen France Germany V lntroduction This book is divided into 9 chapters, which, except for chapter 1, deal with a particu lar aspect of single charge tunneling (SCT) phenomena. Chapter 1 by DEVORET and GRABERT provides an introduction to the other chapters, each of which is to a large extent self-contained. In recent years it has become increasingly clear that the more fun damental objects in the theory of SCT phenomena should be "islands", that is metallic regions with small total capacitance into which electrons can tunnel, rather than indi vidual small capacitance tunnel junctions. Chapter 1 is devoted mainly to the discussion of this idea. Chapter 2 by IN GOLD and N AZAROV deals with the dynamics of ultrasmall junction circuits and teaches one how to compute the tunneling rate of electrons and Cooper pairs across a particular junction in the circuit. Starting with single junction systems, pro gressively more complex cases are treated. In the Appendix, a microscopic justification for the starting hypotheses of the calculations is given. Chapter 3 by ESTEVE explains the basic ideas on which the manipulation of electrons one-by-one in metallic junction circuits are founded. The primary focus is thus on normal junction circuits, although the manipulation of Cooper pairs is briefiy discussed. Particular emphasis is put on the accuracy of devices in which electrons are clocked by an external frequency, such as the "turnstile" and the "electron pump". These devices may lead one day to experiments with metrological accuracy. Chapter 4 by TINKHAM treats the superconducting single junction system. It gives a survey of phenomena observed in low-capacitance tunnel junctions and also provides a link v.ith the usual Josephson effects. Chapter 5 by VAN HOUTEN, BEENAKKER, and STARING deals with semiconductor systems, mostly GaAs/ AlGaA.s heterostructures, in which the metallic islands consist of quasi-isolated regions of the 2D electron gas. In these systems, the interplay between the Coulomb effects and both the Quantum Hall effect and the resonant tunneling effect leads to exciting phenomena. While in the first five chapters single charge tunneling phenomena are analysed mainly in terms of charge tunneling across one junction at a time, Chapter 6 by AVERIN and N AZAROV is a detailed discussion of the process of co-tunneling in which several tunneling events across different junctions occur coherently. Co-tunneling causes fundamentallimi tations of the accuracy of the charge transferring devices described in Chapter 3. Chapters 7 and 8 deal with systems containing a !arge nurober of junctions but which nevertheless display great simplicity because of their translational symmetry properties. Chapter 7 by DELSING treats one-dimensional arrays, with a particular emphasis on RF excitation revealing the self-correlations between tunnel events that exist in sufficiently long arrays. A link with the turnstile of Chapter 3 is made. Chapter 8 by Moou and VII viii lntroduction SCHÖN treats two-dimensional arrays, both in the vortex and the charge regimes. The two-dimensional character of these arrays allows for the possibility of a phase transition. The approximate duality between the vortex and charge regimes is elucidated. Finally, Chapter 9 by AVERIN and LIKHAREV handles the delicate task of predicting the future of the fi.eld. In particular, it discusses the bold and tantalizing claim that digital electronics, in its ultimate stage, will be based on SCT phenomena. Contents 1 Introduction to Single Charge Tunneling by M. H. DEVORET and H. GRABERT 1 1. Basic ingredients of single charge tunneling phenomena 1 2. Single current biased junction 4 3. Single island circuits . . . . . 10 4. Circuits with several islands 15 5. Conclusions 16 References . . . . . . . . . . . . 18 2 Charge Tunneling Rates in Ultrasmall J unctions by G.-L. lNGOLD and Yu. V. NAZAROV 21 1. Introduction . . . . . . . . . . . . . 21 1.1. Ultrasmall tunnel junctions . . . 21 1.2. Voltage-biased tunnel junction . 22 1.3. Charging energy considerations . 23 1.4. Local and global view of a single tunnel junction 24 2. Description of the environment . . . . . . . 25 2.1. Classical charge relaxation . . . . . . 25 2.2. Quantum mechanics of an LC-circuit 26 2.3. Hamiltonian of the environment . . . 28 3. Electron tunneling rates for single tunnel junctions . 30 3.1. Tunneling Hamiltonian . . . . . . . . . . . . . 30 3.2. Calculation of tunneling rates . . . . . . . . . . 31 3.3. Phase-phase correlation function and environmental impedance 36 3.4. General properties of P(E) . . . . . . . . . . . . . . 37 3.5. General properties of current-voltage characteristics 39 3.6. Low impedance environment . . . . . 40 3.7. High impedance environment . . . . . 41 4. Examples of electromagnetic environments 42 4.1. Coupling to a single mode . . . . . . 42 4.2. Ohrnie impedance . . . . . . . . . . 47 4.3. A mode with a finite quality factor . 49 4.4. Description of transmission lines 51 4.5. LC transmission line. 53 4.6. RC transmission line . . . . . . 54 ix X Contents 5. Tunneling rates in Josephson junctions 56 5.1. Introduction . . . . . . . . . . .. 56 5.2. Tunneling of Cooper pairs . . . .. 57 5.3. Charge-phase duality and incoherent tunneling of the phase 60 5.4. Tunneling of quasiparticles ....... . 61 6. Double junction and single electron transistor . 65 6.1. Island charge . . . . . . . . . . ..... . 65 6.2. Network analysis . . . . . . . . ..... . 68 6.3. Tunneling rates in a double junction system . 72 6.4. Double junction in a low impedance environment 73 6.5. Double junction in a high impedance environment 75 6.6. Current-voltage characteristics of a double junction . 77 6.7. Coulomb staircase .......... . 80 6.8. SET-transistor and SET-electrometer 83 6.9. Other multijunction circuits . 86 A. Microscopic foundation 91 A.l. Introduction ... 91 A.2. General problern . 92 A.3. Time of tunneling 97 AA. One-pi10ton processes: anomalies and :fingerprints . 98 A.5. Diffusive anomalies . . . . . . . . . . 99 A.6. Field moves faster than the electrons . 102 A.7. Junction-localized oscillations . 104 A.8. A gateway into networks 105 References . . . . . . . . . . . . . . . . 106 3 Transferring Electrons One By One by D. ESTEVE 109 1. Introduction . . . . . . . . . . . . . . 109 2. Basic concepts of small junction circuits . 110 2.1. Electrons and electronics ..... . 110 2.2. Charge con:figurations . . . . . . . . 111 2.3. Tunneling out of an unstable con:figuration 113 2.4. Co-tunneling out of a locally stable con:figuration 115 2.5. Coexistence of tunneling and co-tunneling 116 3. Single electron box .............. . 117 3.1. Averagecharge in the single electron box 117 3.2. Measurement of the junction charge (Q) 118 3.3. Superconducting case .......... . 122 4. Single electron turnstile . . . . . . . . . . . . . 122 4.1. Basic principles of the controlled transfer of single electrons 122 4.2. The trap: an irreversible single electron box . 123 4.3. From the trap to the turnstile . 124 4.4. Experimental results . 125 4.5. Transfer accuracy . . . . . . . 126
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