Fundamental Problems of Mesoscopic Physics Interactions and Decoherence NATO Science Series A Series presenting the results of scientific meetings supported under the NATO Science Programme. The Series is published by IOS Press, Amsterdam, and Kluwer Academic Publishers in conjunction with the NATO Scientific Affairs Division Sub-Series I. Life and Behavioural Sciences IOS Press II. Mathematics, Physics and Chemistry Kluwer Academic Publishers III. Computer and Systems Science IOS Press IV. Earth and Environmental Sciences Kluwer Academic Publishers V. Science and Technology Policy IOS Press The NATO Science Series continues the series of books published formerly as the NATO ASI Series. The NATO Science Programme offers support for collaboration in civil science between scientists of countries of the Euro-Atlantic Partnership Council. The types of scientific meeting generally supported are “Advanced Study Institutes” and “Advanced Research Workshops”, although other types of meeting are supported from time to time. The NATO Science Series collects together the results of these meetings. The meetings are co-organized bij scientists from NATO countries and scientists from NATO’s Partner countries – countries of the CIS and Central and Eastern Europe. Advanced Study Institutes are high-level tutorial courses offering in-depth study of latest advances in a field. Advanced Research Workshops are expert meetings aimed at critical assessment of a field, and identification of directions for future action. As a consequence of the restructuring of the NATO Science Programme in 1999, the NATO Science Series has been re-organised and there are currently Five Sub-series as noted above. Please consult the following web sites for information on previous volumes published in the Series, as well as details of earlier Sub-series. http://www.nato.int/science http://www.wkap.nl http://www.iospress.nl http://www.wtv-books.de/nato-pco.htm Series II: Mathematics, Physics and Chemistry – Vol. 154 Fundamental Problems of Mesoscopic Physics Interactions and Decoherence edited by Igor V. Lerner University of Birmingham, Birmingham, United Kingdom Boris L. Altshuler Princeton University and NEC Research Institute, Princeton, New Jersey, U.S.A. and Yuval Gefen The Weizmann Institute of Science, Rehovot, Israel KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2193-3 Print ISBN: 1-4020-2192-5 '2004 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer’s eBookstore at: http://www.ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Contents Preface xi Part I Decoherence and Dephasing 1 Electron Dephasing in Mesoscopic Metal Wires 3 Norman O. Birge and F. Pierre 1 Introduction 3 2 τφ in pure Au and Ag samples 5 3 Possible explanations for saturation of τφ 7 4 Aharonov-Bohm experiments in large Cu rings 10 5 Conclusions 13 2 Decoherence effects in the Josephson current of a Cooper pair shuttle 17 Alessandro Romito and Rosario Fazio 1 Introduction 17 2 The model 18 3 Results 20 4 Cooper pair shuttle with SQUID loops 29 3 Dephasing in disordered metals with superconductive grains 33 M. A. Skvortsov, A. I. Larkin, M. V. Feigel’man 1 Introduction 33 2 Description of the formalism 36 3 Dynamics of the phase 37 4 Phase transition 38 5 Cooperon self-energy 40 6 Dephasing time 42 7 Magnetoresistance 44 8 Discussion 45 4 Decoherence in Disordered Conductors at Low Temperatures: the effect 49 of Soft Local Excitations Y. Imry, Z. Ovadyahu and A. Schiller 1 Introduction 50 v vi FUNDAMENTAL PROBLEMS OF MESOSCOPIC PHYSICS 2 The vanishing of the dephasing rate as T →0: theory 51 3 Experimental results 55 4 A tunnelling model for loosely bound heavy impurities 58 5 Conclusions 61 5 Quantum precursor of shuttle instability 65 D. Fedorets, L. Y. Gorelik, R. I. Shekhter and M. Jonson 1 Introduction 65 2 Theoretical model 66 3 Analysis and results 69 6 Dephasing and dynamic localization in quantum dots 75 V.E.Kravtsov 1 Introduction 75 2 Weak dynamic localization 78 3 Role of electron interaction on dynamic localization in closed quan- tum dots. 91 4 Dynamic localization in an open quantum dot and the shape of the Coulomb blockade peak. 93 5 Summary 97 7 Mesoscopic Aharonov-Bohm oscillations in metallic rings 99 T. Ludwig and A. D. Mirlin 1 Introduction 100 2 Low-temperature limit: fully coherent sample 100 3 Dephasing by electron-electron interaction 104 4 Summary 112 8 Influence Functional for Decoherence of Interacting Electrons in Disor- 115 dered Conductors J. von Delft 1 Introduction 115 2 Main results of influence functional approach 118 3 Origin of the Pauli factor 121 4 Calculating τϕ `a la GZ 122 5 Dyson equation and Cooperon self energy 125 6 Vertex contributions 127 7 Discussion and summary 130 Appendix 131 1 Outline of derivation of influence functional 132 2 Cooperon self energy before disorder averaging 135 3 Thermal averaging 136 Contents vii Part II Entanglement and Qubits 9 Low-frequency noise as a source of dephasing of a qubit 141 Y. M. Galperin, B. L. Altshuler and D. V. Shantsev 1 Introduction and model 142 2 Results for a single fluctuator 150 3 Summation over many fluctuators 154 4 Simulations 158 5 Comparison with the noise in the random frequency deviation 162 6 Applicability range of the model 162 7 Conclusions 163 10 Entanglement production in a chaotic quantum dot 167 C.W.J. Beenakker, M. Kindermann, C.M. Marcus, A. Yacoby 1 Introduction 167 2 Relation between entanglement and transmission eigenvalues 169 3 Statistics of the concurrence 171 4 Relation between Bell parameter and concurrence 171 5 Relation between noise correlator and concurrence 172 6 Bell inequality without tunneling assumption 173 7 Conclusion 175 11 Creation and detection of mobile and non-local spin-entangled electrons 179 P. Recher, D. S. Saraga and D. Loss 1 Sources of mobile spin-entangled electrons 179 2 Superconductor-based electron spin-entanglers 180 3 Triple dot entangler 189 4 Detection of spin-entanglement 193 5 Electron-holes entanglers without interaction 197 6 Summary 198 12 Berezinskii-Kosterlitz-Thouless transition in Josephson junction arrays 203 L. Capriotti, A. Cuccoli and A. Fubini, V. Tognetti and R. Vaia 1 Introduction 204 2 The model 205 3 Numerical simulations 206 4 Results 208 5 The phase diagram 212 6 Summary 214 Appendix: PIMC in the Fourier space for JJA 215 Part III Interactions in Normal and Superconducting Systems 13 Quantum coherent transport and superconductivity in carbon nanotubes 219 M. Ferrier, A. Kasumov, R. Deblock, M. Kociak, S. Gueron, B. Reulet and H. Bouchiat 1 Introduction 219 2 Proximity induced superconductivity in carbon nanotubes as a probe of quantum transport 221 3 Intrinsic superconductivity in ropes of SWNT on normal contacts 226 4 Conclusion 235 viii FUNDAMENTAL PROBLEMS OF MESOSCOPIC PHYSICS 14 Quantum Hall ferromagnets, cooperative transport anisotropy, and the 239 random field Ising model J. T. Chalker, D. G. Polyakov, F. Evers, A. D. Mirlin, and P. Wolfle¨ 1 Introduction 240 2 Domain formation and the random field Ising model 242 3 Transport anisotropy arising from domain formation 244 4 Transport along domain walls 247 5 Concluding remarks 249 15 Exotic proximity effects in superconductor/ferromagnet structure 251 F.S.Bergeret, A.F. Volkov and K.B. Efetov 1 Introduction 252 2 The condensate function in a F/S/F sandwich 254 3 Josephson current in a F/S/F/S/F structure 259 4 Effect of spin-orbit interaction 262 5 Induced ferromagnetism in the superconductor 263 6 Summary 270 16 Transport in Luttinger Liquids 275 T. Giamarchi, T. Nattermann and P. Le Doussal 1 Introduction 275 2 Model 276 3 Transport at intermediate temperatures 277 4 Creep 278 5 Variable range hopping 280 6 Open issues 282 17 Interaction effects on counting statistics and the transmission distribution 285 M. Kindermann, Yuli V. Nazarov 18 Variable–range Hopping in One–dimensional Systems 295 J. Prior, M. Ortuno˜ and A. M. Somoza 1 Introduction 295 2 Model 297 3 Model with geometrical fluctuations only 298 4 Hopping matrix elements 301 5 Quantum model 304 6 Fluctuations 305 7 Summary and conclusions 306 19 On the Electron-Electron Interactions in Two Dimensions 309 V. M. Pudalov, M. Gershenson and H. Kojima 1 Introduction 309 2 Renormalized spin susceptibility 311 3 Effective mass and g-factor 318 4 Summary 324 Contents ix 20 Correlations and spin in transport through quantum dots 329 M. Sassetti, F. Cavaliere, A. Braggio and B. Kramer 1 Introduction 329 2 The model 331 3 The characteristic energy scales 333 4 Sequential transport 335 5 Results 339 6 Discussion and conclusion 345 21 Interactions in high-mobility 2D electron and hole systems 349 E. A. Galaktionov, A. K. Savchenko, S. S. Safonov, Y. Y. Proskuryakov, L. Li, M. Pepper, M. Y. Simmons, D. A. Ritchie, E. H. Linfield, and Z. D. Kvon 1 Introduction 349 2 Ballistic regime of electron-electron interaction 351 3 Interaction effects in a 2D hole gas in GaAs 353 4 Electron-electron interaction in the ballistic regime in a 2DEG in Si 361 5 Interaction effects in the ballistic regime in a 2DEG in GaAs. Long- range fluctuation potential. 362 σ 6 Comparison of F0 (rsψ) in different 2D systems 364 7 Conclusion 367 Index 371 Preface The physics of mesoscopic devices came to existence in the mid-eighties when it became apparent that due to the onset of global phase coherence in systems of smaller dimensions, conventional approaches fail to describe sub- micron and nanoscale systems.