Electrons in Solids: Mesoscopics, Photonics, Quantum Computing, Correlations, Topology (Graduate Texts in Condensed Matter)

408 Pages·2019·12.058 MB·English

by  Hendrik Bluhm, Thomas Brückel, Markus Morgenstern, Gero Plessen, Christoph Stampfer

H.Bluhm,T.Brückel,M.Morgenstern,G.vonPlessen,C.Stampfer
ElectronsinSolids
Graduate Texts
in Condensed Matter
|
SeriesEditor
Prof.Dr.ChristianEnss
HeidelbergUniversity
Kirchhoff-InstituteforPhysics
ImNeuenheimerFeld227
69120Heidelberg
Germany

Hendrik Bluhm, Thomas Brückel,
Markus Morgenstern, Gero von Plessen,
Christoph Stampfer
Electrons in Solids
|
Mesoscopics, Photonics, QuantumComputing,
Correlations, Topology
Authors
Prof.Dr.HendrikBluhm Prof.Dr.GerovonPlessen
RWTHAachenUniversity RWTHAachenUniversity
InstituteofPhysics(2C) InstituteofPhysics(1A)
Otto-Blumenthal-Str.28 Otto-Blumenthal-Str.28
52056Aachen,Germany 52056Aachen,Germany
[email protected] [email protected]
Prof.Dr.ThomasBrückel Prof.Dr.ChristophStampfer
ForschungszentrumJülichGmbH/ RWTHAachenUniversity
RWTHAachenUniversity InstituteofPhysics(2A)
FacultyofMathematics,Computer Otto-Blumenthal-Str.28
ScienceandNaturalSciences 52056Aachen,Germany
JCNS-2&PGI-4 [email protected]
52425Jülich,Germany
[email protected]
Prof.Dr.MarkusMorgenstern
RWTHAachenUniversity
InstituteofPhysics(2B)
Otto-Blumenthal-Str.28
52056Aachen,Germany
[email protected]
ISBN978-3-11-043831-4
e-ISBN(PDF)978-3-11-043832-1
e-ISBN(EPUB)978-3-11-042929-9
LibraryofCongressControlNumber:2018955522
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2019WalterdeGruyterGmbH,Berlin/Boston
Coverimage:MarcoPratzer
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Printingandbinding:CPIbooksGmbH,Leck
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Preface
Cuttingedgeresearchinmodernsolidstatephysicsischaracterizedontheonehand
byhighlycomplexsystemswithvariousinteractionsbetweenquasi-particles.Inthis
context,alsoanovelcharacterizationscheme,thatoftopology,hasenteredsolidstate
physicsand allowsnewinsights intothe descriptionofquantum materials.Onthe
otherhand,thereisastrongtendencytotracebacksolidstatephenomenaandsys-
temstotheir quantumphysicalbasis,wherephasecoherence,wavefunctioninter-
ference,superpositionandentanglement playanessentialrole.Thisisparticularly
evidentinresearchonquantumtransportinnanostructuresorinquantumengineer-
ing,wheresolidstatenanosystemsarestudiedwithrespecttoquantuminformation
orsensorapplications.Thesetopicsusuallygobeyondthecontentofstandardcourses
andtextbooksinsolidstatephysics.MyphysicscolleaguesattheRWTHAachenUni-
versity,therefore,haveestablishedanadvancedcourseontopofthebasicsolidstate
physicslectures,wheremasterandPhDstudentsareexposedtotheseimportantfields
of modern research. The present textbook based on this advanced course provides
some topicswhichhave exemplary characterand areparadigmaticfor this kind of
latestcurrentresearchinsolidstatephysics.Fromadeeperunderstandingofthese
examplesotherfieldsofmodernresearcharealsoeasilyaccessible.
Itherefore recommend the book to all those who wantto divedeeper into this
fascinatingfieldofmodernsolidstatephysics,tomasterandPhDstudents,butalso
toscientistsstartinganewresearchfieldandwhowanttolearnsomeessentialsina
reasonablyshorttime.Iwishthebookmuchsuccesssinceitpromotesourbeautiful
science.
HansLüth
JülichAachenResearchAlliance
https://doi.org/10.1515/9783110438321-201

Overview
Thistextbook isthe result of acompulsory, advancedlecture courseinexperimen-
talsolidstatephysicsgivenwithinthemasterscourseatRWTHAachenUniversity.It
goesbeyondtheclassicaltopicsofferromagnetismandsuperconductivity.Thereby,
it bridges the corresponding basic knowledge in solid state physics to more recent
researchtopicssuchastopology or quantum computation.Inparticular,itaimsto
guidestudentsthroughthedifferentlevelsofcomplexityinherentlygivenbythepar-
tiallyclassical,partiallysemiclassicalandpartiallyquantummechanicaldescription
ofsolidstateproperties,wherethelatteroftenemployssimplifiedHamiltoniansasso-
calledtoymodels.Switchingbetweensuchdifferentdegreesofcomplexityisinherent
tosolidstatephysics,sinceafullquantummechanicalsolutionofthemany-particle
problemisnotavailable.Thus,onehastochooseadequateapproximations,strongly
guidedbyexperimentalresults.
Theconceptofthebookistoprovidetheconceptionalskillsneededtoselectan
adequatemodeland,thus,anadequatelevelofcomplexity.Atthesametime,weaim
tofosteranintuitionforthekeypropertiesofdifferenttypesofelectronsystemsunder
differentconditions.Sinceweaddressexperimentalists,weoftenbuildonintuitive,
heuristicargumentsinsteadofrigorouscalculationsand,moreover,alwayscombine
our arguments with experimental results. Thisway ofreasoning providesa key in-
sightintotherequiredinterplaybetweenexperimentsandtheory,whichallowsone
tocorrectlyunderstandthefavorablepropertiesoftheunsolvable,basicSchrödinger
orDiracequations.
Theselectionoftopicsisnotmeanttobeexhaustiveintermsofmodernsolidstate
physics,butprovidesafewdeliberatelychosenexamples,whichrepresentalineof
increasingcomplexity.Westartwithmesoscopics,wherequantummechanicsenters
mainlybythephaseoftheelectronicwavefunctionsrenderingthephasecoherence
thedecisiveterm.Wecontinuewiththedescriptionofopticalpropertiesofsolidstate
electrons,wherepureclassicalelectrodynamicsispartlysufficienttodescribethephe-
nomena.However, thedescriptionof,e.g.,transitionratesalreadyrequirestheuse
ofsuperpositionsofstationaryelectronicstates inacoherent quantummechanical
fashion.Chapter3ofthebookdealswithsolid-statebasedquantumcomputing,ar-
guablythemostimportantemergingapplicationofthequantummechanicaldynam-
icsofsolidstateelectrons.Here,thecoherentquantummechanicaldescriptionofthe
exploiteddegreesoffreedomiskey,whichwilleventuallybeusedforamoreefficient
informationprocessingviasuperpositionstates,i.e.,multiplestationarystatesinpar-
allel.Thehighdegreeofcontrolofthequantummechanicaldynamicsalsoenables
anexperimentalinsightintothetransitionbetweenthequantummechanicalbehav-
ioronthemicroscopicscaleandthephase-freeclassicalbehaviormostlyguidingour
macroscopicscaleexperience.
https://doi.org/10.1515/9783110438321-202
VIII | Overview
InChapter4ofthebook,wetacklethenotoriouslydifficultelectron-electroninter-
actionquantummechanicallyusingthewell-studiedexampleoftransitionmetalox-
ides.WeshowhowsimplifiedtoymodelsoftheSchrödingerequationcaptureessen-
tialpropertiesas,e.g.,thebandgapopening,whichappearsforanominallyhalffilled
single-particleelectronbandduetotheelectron-electroninteraction(Mott–Hubbard
transition).Thetoymodelsstartwithatightbindingdescription,whichreducesthe
single-particleelectronwavefunctionstosingleatoms,beforeintroducingthecom-
plexadditionalterms.Hence,wedealwithpoint-likestartingelectrons,suchthatthe
phaseofthewavefunctionshasaminorinfluenceonthefinalpropertiesofthesys-
tem.Thisapproachchangesinthelastchapterofthebook,wherewedescribeitin-
erant electrons being prone to different types of interactions, namely the electron-
phonon,theelectron-disorderandtheelectron-electroninteraction.Webeginwitha
divergingperturbativeexample,thePeierlstransition.Afterwards,wewillguidestu-
dents through the complex descriptionofband structures via topology. Finally,we
willpresentemergentphenomenaofthemanyparticlecharacterdrivenbytheelec-
tron-electroninteraction,suchasthefractionalchargeofelectronsappearinginfrac-
tionalquantumHallphases.Thelatterdescriptionstressesakeymethodinsolidstate
physics,namelythedescriptionofthesystembyquasiparticleswithaveryabstract
meaning.
Webelievethatthisselectionoftopicssetsthestudentsintoapositiontodealwith
thedifferentlevelsofcomplexity,whicharetypicalforcurrentsolidstateresearch.It
is,moreover,meanttoprovideabasetotackleothermodernresearchtopicssuchas,
e.g., unconventional superconductivity, magnetoelectronics or advanced photonics
employingmetamaterials.Hence,wepresentadedicatedupgradecoursetothewell-
establishedcurriculuminsolidstatephysics.Wehopethatthisnovelapproachrelying
onapartlyheuristicargumentationwillbesuccessfulatotheruniversitiestoo.Being
awareofthefactthatadifferentselectionoftopicsmightbesuitedforthetaskaswell,
weareinterestedinanytypeoffeedback.
WewishtothankFabianHassler,VolkerMeden,andMarcusLiebmannforinsight-
fuldiscussions,HansLüthforveryhelpfulcommentsafteracompletecross-reading
ofthemanuscript,TjorvenJohnsenforcross-readingofsomepartsofthemanuscript,
GereonGraffandFedericaHauptfortakingcareofamultitudeofformalities,Marco
Pratzerfordesigningandmakingthecoverimage,aswellasThomasGraff,Tobias
Cronert,PaulDoege,andJonathanConradforhelpwiththeoptimizationofallother
images.
MarkusMorgenstern(onbehalfofalltheauthors)
RWTHAachenUniversityandJARA-FIT