Electrodynamics of solids: optical properties of electrons in matter

487 Pages·2002·3.733 MB·English

by  Martin Dressel, George Grüner

E LECTRODYNAMICS OF S OLIDS
OPTICAL PROPERTIES OF ELECTRONS IN MATTER
Theauthorsofthisbookpresentathoroughdiscussionoftheopticalpropertiesof
solids,withafocusonelectronstatesandtheirresponsetoelectrodynamicfields. A
review of the fundamental aspects of the propagation of electromagnetic fields, and
theirinteractionwithcondensedmatter,isgiven. Thisisfollowedbyadiscussion
of the optical properties of metals, semiconductors, and collective states of solids
suchassuperconductors.
Theoretical concepts, measurement techniques, and experimental results are
covered in three inter-related sections. Well established, mature fields are dis-
cussed,togetherwithmoderntopicsatthefocusofcurrentinterest. Thesubstantial
referencelistincludedwillalsoprovetobeavaluableresourceforthoseinterested
intheelectronicpropertiesofsolids.
Thebookisintendedforusebyadvancedundergraduateandgraduatestudents,
andresearchersactiveinthefieldsofcondensedmatterphysics,materialsscience,
andopticalengineering.
MARTIN DRESSEL received his Doctor of Sciences degree in 1989 from the
Universita¨t Go¨ttingen where he subsequently worked as a postdoctoral research
fellow. Since then he has held positions in the University of British Columbia at
Vancouver;theUniversityofCalifornia,LosAngeles;theTechnischeUniversita¨t,
Darmstadt; and the Center of Electronic Correlations and Magnetism at the Uni-
versita¨tAugsburg. ProfessorDresselisnowHeadofthe1.PhysikalischesInstitut
attheUniversita¨tStuttgart.
GEORGEGRU¨NERobtainedhisDoctorofSciencesdegreefromtheEo¨tvo¨sLorand
University,Budapest,in1972,andbecameHeadoftheCentralResearchInstitute
of Physics in Budapest in 1974. In 1980 he took up the position of Professor of
Physics at the University of California, Los Angeles, and later became Director
oftheSolidStateScienceCenterthere. ProfessorGru¨nerhasbeenadistinguished
visitingprofessoratnumerousinstitutionsworldwideandisaconsultantforseveral
internationalcorporationsandadvisorypanels. HeisaGuggenheimFellowandis
alsoarecipientoftheAlexanderHumboldtSeniorAmericanScientistAward.
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Electrodynamics of Solids
OpticalPropertiesofElectronsinMatter
MartinDressel
Stuttgart
and
GeorgeGru¨ner
LosAngeles
PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING)
FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge CB2 IRP
40 West 20th Street, New York, NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
http://www.cambridge.org
© Martin Dressel and George Grüner 2002
This edition © Martin Dressel and George Grüner 2003
First published in printed format 2002
A catalogue record for the original printed book is available
from the British Library and from the Library of Congress
Original ISBN 0 521 59253 4 hardback
Original ISBN 0 521 59726 9 paperback
ISBN 0 511 01439 2 virtual (netLibrary Edition)
Contents
Preface pagexi
1 Introduction 1
PART ONE: CONCEPTS AND PROPERTIES 7
Introductoryremarks 7
Generalbooksandmonographs 8
2 Theinteractionofradiationwithmatter 9
2.1 Maxwell’sequationsfortime-varyingfields 9
2.1.1 SolutionofMaxwell’sequationsinavacuum 10
2.1.2 Waveequationsinfreespace 13
2.2 Propagationofelectromagneticwavesinthemedium 15
2.2.1 Definitionsofmaterialparameters 15
2.2.2 Maxwell’sequationsinthepresenceofmatter 17
2.2.3 Waveequationsinthemedium 19
2.3 Opticalconstants 21
2.3.1 Refractiveindex 21
2.3.2 Impedance 28
2.4 Changesofelectromagneticradiationattheinterface 31
2.4.1 Fresnel’sformulasforreflectionandtransmission 31
2.4.2 Reflectivityandtransmissivitybynormalincidence 34
2.4.3 Reflectivityandtransmissivityforobliqueincidence 38
2.4.4 Surfaceimpedance 42
2.4.5 Relationshipbetweenthesurfaceimpedanceandthereflectivity 44
References 45
Furtherreading 46
3 Generalpropertiesoftheopticalconstants 47
3.1 Longitudinalandtransverseresponses 47
v
vi Contents
3.1.1 Generalconsiderations 47
3.1.2 Materialparameters 49
3.1.3 Responsetolongitudinalfields 52
3.1.4 Responsetotransversefields 55
3.1.5 Theanisotropicmedium: dielectrictensor 55
3.2 Kramers–Kronigrelationsandsumrules 56
3.2.1 Kramers–Kronigrelations 57
3.2.2 Sumrules 65
References 69
Furtherreading 70
4 Themedium: correlationandresponsefunctions 71
4.1 Current–currentcorrelationfunctionsandconductivity 72
4.1.1 Transverseconductivity: theresponsetothevectorpotential 73
4.1.2 Longitudinalconductivity: theresponsetothescalarfield 78
4.2 Thesemiclassicalapproach 79
4.3 Responsefunctionformalismandconductivity 81
4.3.1 Longitudinalresponse: theLindhardfunction 81
4.3.2 Responsefunctionforthetransverseconductivity 87
References 91
Furtherreading 91
5 Metals 92
5.1 TheDrudeandtheSommerfeldmodels 93
5.1.1 Therelaxationtimeapproximation 93
5.1.2 OpticalpropertiesoftheDrudemodel 95
5.1.3 DerivationoftheDrudeexpressionfromtheKuboformula 105
5.2 Boltzmann’stransporttheory 106
5.2.1 Liouville’stheoremandtheBoltzmannequation 107
5.2.2 Theq = 0limit 110
5.2.3 Smallqlimit 110
5.2.4 TheChambersformula 112
5.2.5 Anomalousskineffect 113
5.3 Transverseresponseforarbitraryqvalues 115
5.4 Longitudinalresponse 120
5.4.1 Thomas–Fermiapproximation: thestaticlimitforq < k 120
F
5.4.2 SolutionoftheBoltzmannequation: thesmallqlimit 122
5.4.3 Responsefunctionsforarbitraryqvalues 123
5.4.4 Single-particleandcollectiveexcitations 130
5.5 Summaryoftheωdependentandqdependentresponse 132
References 133
Furtherreading 134
Contents vii
6 Semiconductors 136
6.1 TheLorentzmodel 137
6.1.1 Electronictransitions 137
6.1.2 OpticalpropertiesoftheLorentzmodel 141
6.2 Directtransitions 148
6.2.1 Generalconsiderationsonenergybands 148
6.2.2 Transitionrateandenergyabsorptionfordirecttransitions 150
6.3 BandstructureeffectsandvanHovesingularities 153
6.3.1 Thedielectricconstantbelowthebandgap 154
6.3.2 Absorptionneartothebandedge 155
6.4 Indirectandforbiddentransitions 159
6.4.1 Indirecttransitions 159
6.4.2 Forbiddentransitions 162
6.5 Excitonsandimpuritystates 163
6.5.1 Excitons 163
6.5.2 Impuritystatesinsemiconductors 165
6.6 Theresponseforlargeωandlargeq 169
References 171
Furtherreading 171
7 Brokensymmetrystatesofmetals 173
7.1 Superconductinganddensitywavestates 173
7.2 Theresponseofthecondensates 179
7.2.1 Londonequations 180
7.2.2 Equationofmotionforincommensuratedensitywaves 181
7.3 Coherencefactorsandtransitionprobabilities 182
7.3.1 Coherencefactors 182
7.3.2 Transitionprobabilities 184
7.4 Theelectrodynamicsofthesuperconductingstate 186
7.4.1 Cleananddirtylimitsuperconductors,andthespectralweight 187
7.4.2 Theelectrodynamicsforq (cid:3)= 0 188
7.4.3 Opticalpropertiesofthesuperconductingstate:
theMattis–Bardeenformalism 190
7.5 Theelectrodynamicsofdensitywaves 196
7.5.1 Theopticalpropertiesofchargedensitywaves: theLee–Rice–
Andersonformalism 197
7.5.2 Spindensitywaves 198
7.5.3 Cleananddirtydensitywavesandthespectralweight 199
References 202
Furtherreading 203
viii Contents
PART TWO: METHODS 205
Introductoryremarks 205
Generalandmonographs 206
8 Techniques: generalconsiderations 207
8.1 Energyscales 207
8.2 Responsetobeexplored 208
8.3 Sources 210
8.4 Detectors 212
8.5 Overviewofrelevanttechniques 214
References 215
Furtherreading 216
9 Propagationandscatteringofelectromagneticwaves 217
9.1 Propagationofelectromagneticradiation 218
9.1.1 Circuitrepresentation 218
9.1.2 Electromagneticwaves 221
9.1.3 Transmissionlinestructures 223
9.2 Scatteringatboundaries 230
9.2.1 Singlebounce 231
9.2.2 Twointerfaces 233
9.3 Resonantstructures 234
9.3.1 Circuitrepresentation 236
9.3.2 Resonantstructurecharacteristics 238
9.3.3 Perturbationofresonantstructures 241
References 243
Furtherreading 243
10 Spectroscopicprinciples 245
10.1 Frequencydomainspectroscopy 246
10.1.1 Analysis 246
10.1.2 Methods 247
10.2 Timedomainspectroscopy 250
10.2.1 Analysis 251
10.2.2 Methods 253
10.3 Fouriertransformspectroscopy 258
10.3.1 Analysis 260
10.3.2 Methods 264
References 267
Furtherreading 267
Contents ix
11 Measurementconfigurations 269
11.1 Single-pathmethods 270
11.1.1 Radiofrequencymethods 271
11.1.2 Methodsusingtransmissionlinesandwaveguides 273
11.1.3 Freespace: opticalmethods 275
11.1.4 Ellipsometry 278
11.2 Interferometrictechniques 281
11.2.1 Radiofrequencybridgemethods 281
11.2.2 Transmissionlinebridgemethods 282
11.2.3 Mach–Zehnderinterferometer 285
11.3 Resonanttechniques 286
11.3.1 Resonantcircuitsofdiscreteelements 288
11.3.2 Microstripandstriplineresonators 288
11.3.3 Enclosedcavities 290
11.3.4 Openresonators 291
References 295
Furtherreading 297
PART THREE: EXPERIMENTS 299
Introductoryremarks 299
Generalbooksandmonographs 300
12 Metals 301
12.1 Simplemetals 301
12.1.1 ComparisonwiththeDrude–Sommerfeldmodel 302
12.1.2 Theanomalousskineffect 312
12.1.3 Bandstructureandanisotropyeffects 316
12.2 Effectsofinteractionsanddisorder 319
12.2.1 Impurityeffects 319
12.2.2 Electron–phononandelectron–electroninteractions 321
12.2.3 Stronglydisorderedmetals 329
References 336
Furtherreading 337
13 Semiconductors 339
13.1 Bandsemiconductors 339
13.1.1 Single-particledirecttransitions 340
13.1.2 Forbiddenandindirecttransitions 353
13.1.3 Excitons 354
13.2 Effectsofinteractionsanddisorder 357
13.2.1 Opticalresponseofimpuritystatesofsemiconductors 357