Fundamentals of the physics of solids

706 Pages·2007·6.93 MB·English

by  Jenö Sólyom

18 VIIIA 2He21sHelium 10Ne262s2pNeon 18Ar263s3pArgon 36Kr10263d4s4pKrypton 54Xe10264d5s5pXenon 86Rn10265d6s6pRadon
of elements 13 IIIA 14 IVA 15 VA 16 VIA 17 VIIA 5 6 7 8 9BCNOF21222324252s2p2s2p2s2p2s2p2s2pBoronCarbonNitrogenOxygenFluorine 1314151617AlSiPSCl 8 9 1021222324253s3p3s3p3s3p3s3p3s3p 6 VIB 7 VIIBVIIIB 11 IB 12 IIBAluminumSiliconPhosphorusSulfurChlorine 282930313233343524252627NiCuZnGaGeAsSeBrCrMnFeCo8210110210211022102310241025515262723d4s3d4s3d4s3d4s4p3d4s4p3d4s4p3d4s4p3d4s4p3d4s3d4s3d4s3d4sNickelCopperZincGalliumGermaniumArsenicSeleniumBromineChromiumManganeseIronCobalt 464748495051525342434445PdAgCdInSnSbTeIMoTcRuRh1010110210211022102310241025515271814d4d5s4d5s4d5s5p4d5s5p4d5s5p4d5s5p4d5s5p4d4s4d5s4d5s4d5sPalladiumSilverCadmiumIndiumTinAntimonyTelluriumIodineMolybdenumTechnetiumRutheniumRhodium 787980818283848574757677PtAuHgTlPbBiPoAtWReOsIr9110110210211022102310241025425262725d6s5d6s5d6s5d6s6p5d6s6p5d6s6p5d6s6p5d6s6p5d6s5d6s5d6s5d6sPlatinumGoldMercuryThalliumLeadBismuthPoloniumAstatineTungstenRheniumOsmiumIridium 110111106107108109DsRgSgBhHsMt91101425262726d7s6d7s6d7s6d7s6d7s6d7sDarmstadtiumRoentgeniumSeaborgiumBohriumHassiumMeitnerium 646566676869707160616263GdTbDyHoErTmYbLuNdPmSmEu712921021121221321421412425262724f5d6s4f6s4f6s4f6s4f6s4f6s4f6s4f5d6s4f6s4f6s4f6s4f6sGadoliniumTerbiumDysprosiumHolmiumErbiumThuliumYtterbiumLutetiumNeodymiumPromethiumSamariumEuropium 9293949596979899100101102103CmBkCfEsFmMdNoLrUNpPuAm71281210211212213214214123125262725f6d7s5f6d7s5f7s5f7s5f7s5f7s5f7s5f6d7s5f6d7s5f7s5f7s5f7sCuriumBerkeliumCaliforniumEinsteiniumFermiumNobeliumLawrenciumUraniumNeptuniumPlutoniumAmericiumMendelevium
1 IA 11HPeriodic table 11s 2 IIAHydrogen 4 32LiBe12[He] 2s1sLithiumBeryllium 11123NaMg12[Ne] 3s3s 3 IIIB 4 IVB 5 VBSodiumMagnesium 20212223194KCaScTiV12122232[Ar] 4s4s3d4s3d4s3d4sPotassiumCalciumScandiumTitaniumVanadium 38394041375RbSrYZrNb12122241[Kr] 5s5s4d5s4d5s4d5sRubidiumStrontiumYttriumZirconiumNiobium 56577273556CsBaLaHfTa12122232[Xe] 6s6s5d6s5d6s5d6sCesiumBariumLanthanumHafniumTantalum 8788891041057FrRaAcRfDb12122232[Rn] 7s7s6d7s6d7s6d7sFranciumRadiumActiniumRutherfordiumDubnium Lanthanoids5859CePr22324f6s4f6sCeriumPraseodymium 9091 ActinoidsThPa222126d7s5f6d7sThoriumProtactinium
FundamentalsofthePhysicsofSolids
Jeno˝ Sólyom
Fundamentals
of the Physics
of Solids
Volume I
Structure and Dynamics
Translated by Attila Piróth
With240 Figuresand50 Tables
ABC
Author
ProfessorJeno˝ Sólyom
ResearchInstituteforSolidStatePhysics
andOptics
P.O.Box49
1525Budapest
Hungary
and
DepartmentofPhysics
EötvösLorándUniversity
1117Budapest
Pázmánysétány1/A
Hungary
[email protected]
Translator
AttilaPiróth
www.pirothattila.com
TitleoftheHungarianedition:AModernSzilárdtestfizikaAlapjaiI.Aszilárdtestek
szerkezeteésdinamikája,ISBN9634635385,(cid:2)cELTEEötvösKiadó2002
LibraryofCongressControlNumber:2007929725
ISBN978-3-540-72599-2 SpringerBerlinHeidelbergNewYork
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To Márta, Gyöngyvér, Tünde, and lringó
Preface
The reader is holding the first volume of a three-volume textbook on solid-
state physics. This book is the outgrowth of the courses I have taught for
many years at Eötvös University, Budapest, for undergraduate and graduate
studentsunderthetitlesSolid-State Physics andModern Solid-State Physics.
The main motivation for the publication of my lecture notes as a book
was that none of the truly numerous textbooks covered all those areas that
I felt should be included in a multi-semester course. Especially, if the course
strives to present solid-state physics in a unified structure, and aims at dis-
cussing not only classic chapters of the subject matter but also (in more or
less detail) problems that are of great interest for today’s researcher as well.
Besides, the book presents a much larger material than what can be covered
in a two- or three-semester course. In the first part of the first volume the
analysis of crystal symmetries and structure goes into details that certainly
cannotbe includedinausualcourseonsolid-statephysics.Thesameapplies,
among others, to the discussion of the methods used in the determination of
bandstructure,thepropertiesofFermiliquidsandnon-Fermiliquids,andthe
theory of unconventional superconductors in the second and third volumes.
Thesepartscanbeassignedassupplementaryreadingforinterestedstudents,
or can be discussed in advanced courses.
The line of development and the order of the chapters are based on the
prerequisites for understanding each part. Therefore a gradual shift can be
observedinthestyleofthebook.While theintermediatestepsofcalculations
arepresentedinconsiderabledetailandexplanationsarealsomorelengthyin
the first and second volumes, they are much sparser and more concise in the
thirdone,thusthisvolumereliesmoreontheindividualworkofthestudents.
Onaccountoftheprerequisites,certaintopicshavetoberevisited.Thisiswhy
magnetic properties are treated in three, and superconductivity in two parts.
The magnetism of individual atoms is presented in an introductory chapter.
Thestructureanddynamicsofmagneticallyorderedsystemsbuiltupoflocal-
izedmomentsarebestdiscussedafterlattice vibrations,alongthe samelines.
Magnetismisrevisitedinthethirdvolume,wheretheroleofelectron–electron
VIII Preface
interactions is discussed in more detail. Similarly, the phenomenological de-
scription of superconductivity is presented after the analysis of the transport
propertiesofnormalmetals,incontrasttothem,whilethemicroscopictheory
is outlined later, when the effects of interactions are discussed.
Separating the material into three similar-sized volumes is a necessity in
view of the size ofthe material– but it also reflects the internallogicalstruc-
ture of the subject matter. At those universities where the basic course in
solid-state physics runs for three semesters working through one volume per
semesterisanaturalschedule.Inthiscasethediscussionoftheelectrongas–
whichistraditionallypartoftheintroduction–isleftforthesecondsemester.
Thischoiceisparticularlysuitedtocurriculainwhichthecourseonsolid-state
physics is held parallel with quantum mechanics or statistical physics. If the
lecturer feels more comfortable with the traditional approach, the discussion
of the Drude model presented in the second volume can be moved to the be-
ginning of the whole course. Nevertheless the discussion of the Sommerfeld
model should be postponed until students have familiarized themselves with
the fundamentals of statistical physics. For the same reasonthe lecturer may
prefer to change the order of other chapters as well. Apart from the presen-
tation of the consequences of translational symmetry, the topics discussed in
Chapters 3, 4, and 6 can be deferred to a later time, when students have
acquired a sound knowledge of quantum mechanics, atomic, and molecular
physics.The consequencesoftranslationalsymmetrycanalsobe analyzedaf-
ter the discussionofphonons.Allthis is,to a largeextent,up to the personal
preferences of the lecturer.
In presenting the field of solid-state physics, special emphasis has been
laid on discussing the physical phenomena that can be observed in solids.
Nevertheless I have tried to give – or at least outline – the theoretical inter-
pretation for each phenomenon, too. As is common practice for textbooks, I
have omitted precise references that would give the publication data of the
discussed results. I have made exceptions only for figures taken directly from
published articles. At the end of the first, introductory chapter I have given
a list of textbooks and series on solid-state physics, while at the end of each
subsequent chapter I have listed textbooks and review articles that present
further details and references pertaining to the subject matter of the chapter
in question.
Bulky as it might be, this three-volume treatise presents only the funda-
mentals of solid-state physics. Today, when articles about condensed matter
physics fill tens of thousands of pages every year in Physical Review alone, it
would be obviously overambitiousto aim at more. Therefore,building on the
foundationspresentedinthis book students willhaveto acquireasubstantial
amount of extra knowledge before they can understand the subtleties of the
topicsintheforefrontoftoday’sresearch.Neverthelessattheendofthethird
volume students will also appreciate the number of open questions and the
necessity of further research.
Preface IX
A certain knowledge of quantum mechanics is a prerequisite for studying
solid-statephysics.Varioustechniquesofquantummechanics–aboveallfield-
theoretical methods and methods employed in solving many-body problems
– play an important role in present-day solid-state physics. Some essential
detailsarelistedinoneoftheappendicesofthethirdvolume,however,Ihave
omitted more complicated calculations that would have required the applica-
tion of the modern apparatus of many-body problems.This is especially true
for the third volume, where central research topics of present-day solid-state
physics are discussed, in which the theoretical interpretation of experimen-
tal results is often impossible without some extremely complex mathematical
formulation.
The selection of topics obviously bears the stamp of the author’s own re-
search interest, too. This explains why the discussion of certain important
fields–suchasthemechanicalpropertiesofsolids,surfacephenomena,amor-
phoussystemsormesoscopicsystems,tonamebutafew–havebeenomitted.
I have used the International System of Units (SI), and have given the
equationsofelectromagnetisminrationalizedform.Nonrationalizedequations
as well as gaussian CGS (and other) units are nevertheless still very much in
useinthe solid-statephysicsliterature.Thishasbeenindicatedattheappro-
priateplaces.OnafewoccasionsIhavealsogiventheformulasobtainedfrom
nonrationalizedequations. In addition to the fundamental physical constants
used in solid-state physics, the commonest conversion factors are also listed
in Appendix A. Only once have I deviated from standard practice, denoting
Boltzmann’s constant by k instead of k – reserving the latter for the wave
B
number, which plays a central role in solid-state physics.
To give an impression of the usual values of the quantities occurring in
solid-statephysics,typicalcalculatedvaluesormeasureddataareoftentabu-
lated.Toprovidethemostprecisedataavailable,IhavereliedontheLandolt–
Börnstein series, the CRC Handbook of Chemistry and Physics, and other
renowned sources. Since these data are for information only, I have not indi-
cated either their error or in many cases the measurement temperature, and
I have not mentioned when different measurement methods lead to slightly
disparate results. As a rule of thumb, the error is usually smaller than or on
the order of the last digit.
I would like to thank all my colleagues who read certain chapters and
improved the text through their suggestions and criticism. Particular thanks
go to professors György Mihály and Attila Virosztek for reading the whole
manuscript. In spite of all efforts, some mistakes have certainly remained in
the book. Obviously, the author alone bears the responsibility for them.
Special thanks are due to Károly Härtlein for his careful work in draw-
ing the majority of the figures. The figures presenting experimental results
are reproduced with the permission of the authors or the publishers. M. C.
Escher’s drawings in Chapter 5 are reproduced with the permission of the
copyrightholder©2006The M.C.EscherCompany-Holland.The challenge
X Preface
of translating the book from the Hungarian original was taken up by Attila
Piróth. I acknowledge his work.
Finally, I am indebted to my family, to my wife and children, for their
patience during all those years when I spent evenings and weekends with
writing this book.
Budapest, May 2007 Jenő Sólyom