Collective Excitations in Solids

716 Pages·1983·20.051 MB·English

by  F. Williams (auth.), Baldassare Di Bartolo (eds.)

Collective Excitations in Solids
NATO Advanced Science Institutes Series
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edited by Vu Thien Binh
Vo/ume 87 -Relativistic Effects in Atoms, Molecules, and Solids
edited by G. L. Malli
Vo/ume 88 -Collective Excitations in Solids
edited by Baldassare Di Bartolo
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Vo/ume 89b-Electrical Breakdown and Discharges in Gases: Macroscopic
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edited by Erich E. Kunhardt and Lawrence H. Luessen
Collective Excitations in Solids
Edited by
Baldassare Di Bartolo
Boston College
Chestnut Hili, Massachusetts
Assistant Editor
Joseph Danko
Boston College
Chestnut Hili, Massachusetts
Plenum Press
New York and London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of the NATO Advanced Study Institute on
Collective Excitations in Solids,
held June 15-29, 1981,
in Erice, Italy
Library of Congress Cataloging in Publication Data
NATO Advanced Study Institute on Collective Excitations in Solids (1981: Erice, Italy)
Collective excitations in solids.
(NATO advanced science institutes series. Se ries B, Physics; v. 88)
"Proceedings of the NATO Advanced Study Institute on Collective Excitations in Solids,
held June 15-29, 1981, in Erice, Italy"-P.
Includes bibliographical references and index.
1. Collective excitations-Congresses. 2. Exciton theory-Congresses. I. Di Bartolo,
Baldassare. 11. Danko, Joseph. 111. North Atlantic Treaty Organization. Scientific Affairs Divi
sion. IV. Title. V. Series.
QC176.8.E9N361981 530.4'1 82-18928
ISBN 978-1-4684-8880-7 ISBN 978-1-4684-88784 (eBook)
00110.1007/978-14684-88784
© 1983 Plenum Press, New Vork
Softcover reprint of the hanlcover 1st edition 1983
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PREFACE
This book presents an ac count of the NATO Advanced Study
Institute on "Collective Excitations in Solids," held in Erice,
Italy, from June 15 to June 29, 1981. This meeting was organized
by the International School of Atomic and Molecular Spectroscopy
of the "Ettore Majorana" Centre for Scientific Culture.
The objective of the Institute was to formulate a unified and
coherent treatment of various collective excitation processes by
drawing on the current advances in various branches of the physics
of the solid state.
A total of 74 participants came from 54 laboratories and 20
nations (Australia, Belgium, Burma, Canada, China, France, F. R.
Germany, Greece, Israel, Italy, Mexico, The Netherlands, Pakistan,
Poland, Portugal, Romania, Switzerland, Turkey, The Uni ted Kingdom,
and The United States). The secretaries of the course were:
Joseph Danko for the scientific aspects and Nino La Francesca for
the administrative aspects of the meeting.
Fourty-four lectures divided in eleven series were given.
Nine "long" seminars and eight "short" seminars were also presented.
In addition, two round-table discussions were held.
The Institute was concerned first with establishing the frame
work required for describing the physical processes resulting in
the collective excitations of asolid; this task was the respons i
bility of the first three lecturers. Once the basic principles
were established, the other lecturers developed in detail specific
treatments of the various types of collective excitations. For
example, one lecturer treated vibrations in solids (phonons),
another the excitations resulting from the perturbation of a
system of locked and aligned spins (magnons), etc. The subject of
excitons included a general treatment and a more detailed examina
tion of specific cases. Other excitations such as plasmons,
polarons and polaritons were also treated.
vii
viii PREFACE
Specific aspects of the theory were also presented in seminar
form together with several applications to various areas of cur
rent interest.
Professor Williams led the attendees during the final session
which considered a synthesis of the material presented in the
lectures and identified directions of profitable efforts.
I would like to thank their help Dr. A. Gabriele, Ms. P.
Savalli, and all the personnel of the "Ettore Majorana" organi
zation in Erice, Prof. R. L. Carovillano, Chairman of the
Depa:tment of Physics at Boston College, Prof. V. Adragna,
Dr. G. Denaro, Rag. M. Strazzera, and Avv. G. Luppino.
I would like to thank for their help Prof. A. Zichichi,
Director of the "Ettore Majorana" Centre for Scientific Culture,
Dr. A. Gariele, Ms. P. Savalli, and all the personnel of the
"Ettore Majorana" organization in Erice, Prof. R. L. Carovillano,
Chairman of the Department of Physics at Boston College, Prof.
V. Adragna, Dr. G. Denaro, Rag. M. Strazzera, and Avv. G. Luppino.
I would like to thank the members of the organizing committee
(Profs. Williams and Scharmann), Prof. Knox, and Dr. Auzel for their
valuable help and advice.
I am especially grateful to my friend and collaborator,
A. La Francesca, who helped me tremendously during the two weeks
of the meeting, and to J. Danko for his help during the meeting
and for his patient and intelligent work as assistant editor of
this book.
I am looking forward to the next meeting of our school in
1983 and to a new occasion to meet again in Erice many of the fine
people with whom I shared the experience of this Institute.
Arrivederci, my friends!
B. Di Bartolo
Editor and Director of
the Institute
Erice, June 1981
CONTENTS
QUANTUM MECHANICAL DESCRIPTION OF SOLIDS
F. Williams
Abstract ---------------------------------------------------- 1
I. Introduction ----------------------------------------- 2
11. Adiabatic Approximation ------------------------------ 3
111. Hartree-Fock Approximation --------------------------- 5
IV. Electronic Bands in Crystals ------------------------- 6
V. Lattice Dynamics as Collective
Excitations: Phonons -------------------------------- 9
VI. Collective Excitations of Electrons:
Plasmons --------------------------------------------- 11
VII. Extrinsic States ------------------------------------- 12
VIII. Some Effects of Applied Stress ----------------------- 15
IX. Conclusions ------------------------------------------ 17
References -------------------------------------------------- 17
INTRODUCTION TO COLLECTlVE EXCITATIONS IN SOLIDS
B. Di Bartolo
Abstract ---------------------------------------------------- 19
I. Interactions in a Two-Level System ------------------- 19
I.A. Quantum-Mechanical Resonance ------------------- 19
I.B. Static Effects of Perturbation ----------------- 24
11. Collective Excitations ------------------------------- 29
II.A. Setting of the Problem ------------------------ 29
II.B. Eigenfunctions -------------------------------- 31
II.C. Dispersion Relations -------------------------- 37
II.D. Effective Mass -------------------------------- 39
II.E. Generalization to Three Dimension ------------- 40
II.F. Periodic Boundary Conditions and
Density of States ----------------------------- 43
ix
x CONTENTS
111. Interaction of Radiation with Co11ective
Excitations 47
III.A. The Radiation Fie1d ------------------------- 47
1. The C1assical Radiation Field ----------- 47
2. The Quantum Radiation Fie1d ------------- 49
III.B. The Form of the Interaction ------------------ 52
III.C. Absorption and Emission Processes ----------- 53
III.D. Interaction of Photons with
Collective Excitations ----------------------- 56
IV. Propagation of Radiation in a Dispersive Medium ------ 58
IV.A. Introduction ---------------------------------- 58
IV.B. Dielectric Constant --------------------------- 60
IV.C. Propagation of Electromagnetic Waves
in a Dispersive Medium ------------------------ 62
V. Examples of Collective Excitations ------------------- 70
V.A. Phonons ---------------------------------------- 70
1. Summary of Properties ---------------------- 70
2. Infrared Absorption by Ionic Solids -------- 71
V.B. Excitons --------------------------------------- 74
1. General Theory ----------------------------- 74
2. The Frenkel Exciton ------------------------ 79
3. The Wannier Exciton ------------------------ 85
4. The Intermediate Case ---------------------- 89
5. The Photon-Exciton System ------------------ 89
6. The Photon-Exciton-Phonon System ----------- 91
7. Indirect Transitions ----------------------- 91
V.C. Magnons ---------------------------------------- 94
1. Setting of the Problem --------------------- 94
2. Hamiltonian and Eigenstates ---------------- 95
3. Semic1assical Treatment -------------------- 100
4. Thermodynamics of Magnons ------------------ 102
V.C. Plasmons --------------------------------------- 105
1. Dielectric Response of an Ensemble
of Oscillators ----------------------------- 105
2. Die1ectric Response of a Free
Electron Gas ------------------------------- 108
3. Transversal Optical Modes in a Plasma ------ 109
4. Longitudinal Optical Modes in a Plasma ----- 112
References -------------------------------------------------- 114
QUASI-PARTICLES AND EXCITONS: MODELS OF STRUCTURE
AND CORRELATION
G. Mahler
Abstract ---------------------------------------------------- 115
I. Introduction ---------------------------------------- 115
CONTENTS xi
11. Basic Concepts of Quantum Fie1d Theory ------------- 116
II.A. Quantization of C1assica1 Fie1ds ------------ 116
II.B. Schrödinger Fie1d --------------------------- 119
II.C. Occupation Number Representation ------------- 121
II.D. Se1f-Interaction ------------------------____ _ 122
II.E. Sources ---------------------------------____ _ 123
II.F. Effective Vacuum ----------------------------- 124
111. Models 126
III.A. Empty Band Model --------------------------- 126
III.B. Fermi Gas Model ---------------------------- 127
III.C. Tight Binding Model (TBM) ------------------ 130
III.D. Models with Partic1e Interactions ---------- 132
III.E. Random Ce11 Model (RCM) -------------------- 134
III.F. Driven Systems ------------------------------ 139
IV. Conc1usions ----------------------------------------- 148
References -------------------------------------------------- 148
COHERENT WAVEPACKETS OF PHONONS
N. Terzi
Abstract ---------------------------------------------------- 149
I. One-Dimensiona1 E1astic Line ------------------------ 149
I.A. Monatomic Array of Rigid Atoms ---------------- 150
I.B. Forces ---------------------------------------- 151
I.C. Energy ---------------------------------------- 153
1. Potential Energy -------------------------- 153
2. Kinetic Energy ---------------------------- 156
3. Total Energy ------------------------------ 157
I.D. Continuous Vibrating Line --------------------- 157
11. Beyond the Model of a Chain of Masses
and Springs ----------------------------------------- 159
111. Motion of a Pulse in the C1assica1 Limit ------------ 160
III.A. General Features ---------------------------- 160
III.B. Pulse Shape and Dispersion ------------------ 161
IV. Motion of a Pulse in Quantum Mechanics -------------- 162
IV.A. Variables ------------------------------------ 162
IV.B. Phonons and Phonon Wavepackets -------------- 164
IV.C. Propagation of a Pulse: Moment
and Energy ----------------------------------- 165
1. Moment ----------------------------------- 166
2. Energy ----------------------------------- 166
V. Birth and Death of a Pulse -------------------------- 167
References -------------------------------------------------- 167