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Quantum Kinetic Theory and Applications

Electrons, Photons, Phonons

Quantum Kinetic Theory and Applications

Electrons, Photons, Phonons

FEDIR T. VASKO OLEG E. RAICHEV

Institute of Semiconductor Physics NAS of Ukraine, Kiev

Fedir T. Vasko Oleg E. Raichev Institute of Semiconductor Physics, NAS Institute of Semiconductor Physics, NAS 45 Prospekt Nauki 45 Prospekt Nauki Kiev 03028 Ukraine Kiev 03028 Ukraine

Library of Congress Control Number: 2005926337

ISBN-10: 0-387-26028-5 e-ISBN: 0-387-28041-3 ISBN-13: 978-0387-26028-0

Printed on acid-free paper.

©2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

Printed in the United States of America. (HAM)

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Preface

Physical kinetics is the final section of the course of theoretical physics in its standard presentation. It stays at the boundary between gen- eral theories and their applications (solid state theory, theory of gases, plasma, and so on), because the treatment of kinetic phenomena always depends on specific structural features of materials. On the other hand, the physical kinetics as a part of the quantum theory of macroscopic systems is far from being complete. A number of its fundamental is- sues, such as the problem of irreversibility and mechanisms of chaotic responses, are now attracting considerable attention. Other important sections, for example, kinetic phenomena in disordered and/or strongly non-equilibrium systems and, in particular, phase transitions in these systems, are currently under investigation. The quantum theory of mea- surements and quantum information processing actively developing in the last decade are based on the quantum kinetic theory.

Because a deductive theoretical exposition of the subject is not con- venient, the authors restrict themselves to a lecture-style presentation. Now the physical kinetics seems to be at the stage of development when, according to Newton, studying examples is more instructive than learn- ing rules. In view of these circumstances, the methods of the kinetic theory are presented here not in a general form but as applications for description of specific systems and treatment of particular kinetic phe- nomena.

The quantum features of kinetic phenomena can arise for several rea- sons. One naturally meets them in strongly correlated systems, when it is impossible to introduce weakly interacting quasiparticles (for exam- ple, in a non-ideal plasma), or in more complicated conditions, such as in the vicinity of the phase transitions. Next, owing to complexity of the systems like superconductors, ferromagnets, and so on, the manifes- tations of kinetic phenomena change qualitatively. The theoretical con-

v

vi QUANTUM KINETIC THEORY

sideration of these cases can be found in the literature. Another reason for studying quantum features of transport and optical phenomena has emerged in the past decades, in connection with extensive investigation of kinetic phenomena under strong external fields and in nanostructures. The quantum features of these phenomena follow from non-classical dy- namics of quasiparticles, and these are the cases the present monograph takes care of, apart from consideration of standard problems of quan- tum transport theory. Owing to intensive development of the physics of nanostructures and wide application of strong external (both stationary and time-dependent) fields for studying various properties of solids, the theoretical methods presented herein are of current importance for anal- ysis and interpretation of the experimental results of modern solid state physics.

This monograph is addressed to several categories of readers. First, it will be useful for graduate students studying theory. Second, the top- ics we cover should be interesting for postgraduate students of various specializations. Third, the researchers who want to understand the back- ground of modern theoretical issues in more detail can find a number of useful results here. The phenomena we consider involve kinetics of electron, phonon, and photon systems in solids. The dynamical prop- erties and interactions of electrons, phonons, and photons are briefly described in Chapter 1. Further, in Chapters 2−8, we present main the- oretical methods: linear response theory, various kinetic equations for the quasiparticles under consideration, and diagram technique. The pre- sentation of the key approaches is always accompanied by solutions of concrete problems, to illustrate applications of the theory. The remain- ing chapters are devoted to various manifestations of quantum transport in solids. The choice of particular topics (their list can be found in the Contents) is determined by their scientific importance and methodolog- ical value. The 268 supplementary problems presented at the end of the chapters are chosen to help the reader to study the material of the mono- graph. Focusing our attention on the methodical aspects and discussing a great diversity of kinetic phenomena in line with the guiding principle “a method is more important than a result,” we had to minimize both detailed discussion of physical mechanisms of the phenomena considered and comparison of theoretical results to experimental data.

It should be emphasized that the kinetic properties are the impor- tant source of information about the structure of materials, and many peculiarities of the kinetic phenomena are used for device applications. These applied aspects of physical kinetics are not covered in detail either. However, the methods presented in this monograph provide the theoret- ical background both for analysis of experimental results and for device

PREFACE vii

simulation. In the recent years, these theoretical methods were applied for the above-mentioned purposes so extensively that any comprehensive review of the literature seems to be impossible in this book. For this reason, we list below only a limited number of relevant monographs and reviews.

Fedir T. Vasko Oleg E. Raichev Kiev, December 2004

Monographs: 1. J. M. Ziman, Electrons and Phonons, the Theory of Transport Phenomena in

Solids, Oxford University Press, 1960. 2. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, W. A. Benjamin,

Inc., New York, 1962. 3. A. A. Abrikosov, L. P. Gor’kov and I. E. Dzialoszynski, Methods of Quantum

Field Theory in Statistical Physics, Prentice-Hall, 1963. 4. S. Fujita, Introduction to Non-Equilibrium Quantum Statistical Mechanics,

Saunders, PA, USA, 1966. 5. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, Consultants Bu-

reau, New York, 1974. 6. E. M. Lifshitz and L. P. Pitaevski, Physical Kinetics, Pergamon Press, Oxford,

1981. 7. H. Bottger and V. V. Bryksin, Hopping Conduction in Solids, VCH Publishers,

Akademie-Verlag Berlin, 1985. 8. V. L. Gurevich, Transport in Phonon Systems (Modern Problems in Condensed

Matter Sciences, Vol. 18), Elsevier Science Ltd., 1988. 9. V. F. Gantmakher and Y. B. Levinson, Carrier Scattering in Metals and Semi-

conductors (Modern Problems in Condensed Matter Sciences, Vol. 19), Elsevier Sci- ence Ltd., 1987.

10. A. A. Abrikosov, Fundamentals of the Theory of Metals, North-Holland, 1988. 11. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic

Properties of Semiconductors, World Scientific, Singapore, 1990. 12. N. N. Bogolubov, Introduction to Quantum Statistical Mechanics, Gordon and

Breach, 1992. 13. G. D. Mahan, Many Particle Physics, Plenum, New York, 1993. 14. H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of

Semiconductors, Springer, Berlin, 1997. 15. Y. Imry, Introduction to Mesoscopic Physics, Oxford University Press, 1997. 16. D. K. Ferry and S. M. Goodnick, Transport in Nanostructures, Cambridge

University Press, New York, 1997. 17. R. P. Feynmann, Statistical Mechanics, Addison-Wesley, 1998. 18. A. M. Zagoskin, Quantum Theory of Many-Body Systems: Techniques and

Applications, Springer-Verlag, New York, 1998. 19. F. T. Vasko and A. V. Kuznetsov, Electron States and Optical Transitions in

Semiconductor Heterostructures, Springer, New York, 1998.

viii QUANTUM KINETIC THEORY

20. J. Rammer, Quantum Transport Theory (Frontiers in Physics, Vol. 99), West- view Press, 1998.

21. T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zverger, Quantum Transport and Dissipation, Wiley-VCH, Weinheim, 1998.

22. B. K. Ridley, Quantum Processes in Semiconductors, Oxford University Press, 1999.

23. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Infor- mation, Springer, Berlin, Heidelberg, New York, 2000.

Reviews: 1. D. N. Zubarev, Double-Time Green’s Functions, Sov. Phys. - Uspekhi 3, 320

(1960). 2. R. N. Gurzhi and A. P. Kopeliovich, Low-Temperature Electrical Conductivity

of Pure Meta