Strong and Weak Topology Probed by Surface Science: Topological Insulator Properties of Phase Change Alloys and Heavy Metal Graphene

172 Pages·2015·8.23 MB·English

by  Christian Pauly (auth.)

MatWerk
Edited by
Dr.-Ing. Frank O. R. Fischer (Deutsche Gesellschaft für Materialkunde e.V.)
Frankfurt am Main, Deutschland
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Herausgeber/Editor:
Dr.-Ing. Frank O. R. Fischer (Deutsche Gesellschaft für Materialkunde e.V.)
Frankfurt am Main, Deutschland
Christian Pauly
Strong and Weak
Topology Probed
by Surface Science
Topological Insulator Properties
of Phase Change Alloys and
Heavy Metal Graphene
123
Christian Pauly
Aachen, Germany
D 82 (Diss. RWTH Aachen University, [2015])
MatWerk
ISBN 978-3-658-11810-5 ISBN 978-3-658-11811-2 (eBook)
DOI 10.1007/978-3-658-11811-2
Library of Congress Control Number: 2015957085
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Acknowledgments
I would like to thank all the people that contributed to this work and who
gavemethenecessarysupportinordertosuccessfullyfinishmyPhDthesis.
First,IsincerelyacknowledgeProf.Dr.MarkusMorgensternwhogavemethe
opportunitytodothisworkwithinhisgroup. Hisconstantsupportaswell
as his permanent willingness of discussion ensured a pleasant work envi-
ronment. Hisenthusiasmconcerningallkindofscientificquestionstogether
withhisbroadknowledgeinsurfacescienceencouragedandhelpedmealot
inordertoimprovemyownscientificunderstandingandskills.Thisabilities
hasledtoaveryproductiveandenjoyableworkingenvironmentwithinthe
wholegroupandwhichishardtofind.
Special thanks go to the Fonds National de la Recherche (FNR) Luxembourg
whichfundedmyresearchstayatthegroupofProf.Morgensternandwhich
gavemetheopportunitytostartandsuccessfullyfinishmyPhDthesis.Espe-
cially,theveryuncomplicatednatureoftheFNRadministrationstaffenabled
apleasantandsmoothcommunicationprocessforallkindofquestions.
ManythankstomydirectsupervisorDr.MarcusLiebmann,whohelpedme
alotinunderstandingspecialtheoreticalandexperimentalproblemswithin
myresearchfield. Especiallyintheevaluationofmydata,hewasveryhelp-
fulandcontributedalottotheoutcomeofthisthesis. Further, weshareda
pleasantandfruitfultimeinandoutsidethebeamlineduringourstaysatthe
synchrotronBESSYinBerlin.
Next,IwouldliketothankmyformermasterstudentsMartinGrobandJens
KellneraswellasmyofficemateAlexGeorgiwhichwhomIspentapleasant
timeattheinstituteandonotheroccasions.
I also thank Dr. Dinesh Subramaniam and compatriot Mike Pezzotta who, es-
peciallyatthebeginningofmyPhDtime,facilitatemyintroductionintothe
field of condensed matter physics and scanning tunneling microscopy. We
havestayedgreatcolleaguesandfriendseversince.
For the great atmosphere in and outside the institute as well as for many
helpful hands during my PhD work, I gratefully acknowledge Dr. Marco
Pratzer,RaphaelBindel,ChristianSaunus,KilianFlöhr,NilsFreitag,SilkeHatten-
dorf,FlorianMuckel,DanielMontag,Dr.PeterNemes-Incze,Dr.ViktorGeringer,
Dr.StefanBecker,Dr.TorgeMashoff,SvenJust,BernhardKaufmann,TjorvenJohn-
sonandFelixJekat.
VI Acknowledgments
Specialthanksgotoourcooperationpartnerswhocontributedwithlarger
and smaller assists to the successful completion of the different projects de-
scribedinthisthesis.ThepeopleofthegroupofProf.Dr.OliverRaderfromthe
Helmholtz-ZentrumBerlinwhointroducedusintothefieldofangle-resolved
photoemissionspectroscopyandintensivelysupportedusduringourseveral
stays at the synchrotron BESSY. The group of Dr. Raffaella Calarco and espe-
ciallyDr.AlessandroGiussaniandDr.JosBoschkerfromthePaul-Drudeinsti-
tute in Berlin for the high-quality growing and pre-characterization of the
differentphasechangematerials. Dr.GustavBihlmayerfromthePeterGrün-
bergInstitutoftheForschungszentrumJülichforthetheoreticalbackground
inthefieldofSb Te andGe Sb Te andhispartlyextremelyfasthelpwith
2 3 2 2 5
DFTdataandtheirinterpretation. BertoldRaschefromthegroupofProf.Dr.
MichaelRuckinDresden,providingustheBi Rh I samplestogetherwitha
14 3 9
broadknowledgeinthefieldofspecificchemistryofmaterialsandthepeople
ofthegroupofProf.Dr.JeroenvandenBrinkfromtheIFWinDresden,namely
Dr.ManuelRichterandDr.KlausKoepernikwhichperformedtheadequatethe-
oreticalcalculationsforthisparticularmaterial.
IthankProf.Dr.ThomasSchäpersfortheco-evaluationofmythesis.
Further, I acknowledge Jörg Schirra and Sascha Mohr for the continuous
supplyofhelium. EspeciallytheChristmashelium-supportrequiresahuge
gratefulness.
Manythanksgoouttothemechanicalworkshopunderthesupervisionof
PeterKordtandWolfgangRetetzkifortheirremarkableandquickfabricationof
allkindofcomponentswithhighprecisionandquality.
IalsowanttothanktheadministrativestaffoftheII.instituteinpersonof
MargareteBetger,BeatrixDangela,NinaGrydzhukandBeateNagelfortheeasy
anduncomplicatedhandlingofallkindofadministrationinadditiontothe
verypleasantandagreeableatmosphereintheiroffice.
Last but not least, I thank Sophie Hellinghausen for her constant support
during my PhD thesis which included good and less good times, and my
parentsJosianeandCharlesPaulywhosupportedmeinanywaytheycould.
Merci!
ChristianPauly
Contents
Acknowledgments V
1 Introduction 1
2 FundamentalsofTopologicalInsulators 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Insulatorswithmetallicboundarystates . . . . . . . . . . . . . . 5
2.2.1 IntegerquantumHalleffect . . . . . . . . . . . . . . . . . 7
2.2.2 TheHallconductanceasatopologicalinvariant . . . . . 8
2.2.3 QuantumspinHalleffectortime-reversalinvariant2D
topologicalinsulator . . . . . . . . . . . . . . . . . . . . . 14
2.2.4 ConstructionofZ invariantfor2Dtopologicalinsulators 19
2
2.2.5 Generalizationtothree-dimensions . . . . . . . . . . . . 29
2.2.6 Weaktopologicalinsulators . . . . . . . . . . . . . . . . . 34
2.2.7 Experimentalrealizationsof3Dtopologicalinsulators . 36
3 ExperimentalMethods 41
3.1 Scanningtunnelingmicroscopy . . . . . . . . . . . . . . . . . . . 41
3.1.1 Tersoff-Hamannmodel . . . . . . . . . . . . . . . . . . . 42
3.1.2 Scanningtunnelingspectroscopy . . . . . . . . . . . . . . 44
3.1.3 STMandSTSexperiments . . . . . . . . . . . . . . . . . . 46
3.2 Angle-resolvedphotoemissionspectroscopy . . . . . . . . . . . 47
3.2.1 Spin-resolvedARPES . . . . . . . . . . . . . . . . . . . . 53
3.2.2 Experimentaldetails:ARPESatthesynchrotron . . . . . 55
4 IdentificationofTelluriumbasedPhase-ChangeMaterialsasStrong
TopologicalInsulators 59
4.1 Fundamentalsofphase-changematerials . . . . . . . . . . . . . 60
4.2 Identificationoftopologicalinsulatorpropertiesincrystalline
Sb Te . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2 3
4.2.1 STMandSTScharacterizationofSb Te . . . . . . . . . . 65
2 3
4.2.2 Spin-resolvedARPESmeasurementsofSb Te . . . . . . 74
2 3
VIII Contents
4.3 Characterization of crystalline Ge Sb Te in terms of
2 2 5
topologicalinsulator . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.1 StackingorderofGe Sb Te inthecrystallinephase . . . 90
2 2 5
4.3.2 Preparation and characterization of metastable
crystallineGe Sb Te samples . . . . . . . . . . . . . . . 92
2 2 5
4.3.3 Evidence for topological band inversion in metastable
crystallineGe Sb Te measuredbyARPES . . . . . . . . 95
2 2 5
5 WeakTopologicalInsulator 105
5.1 General description of the first synthesized weak topological
insulatorBi Rh I . . . . . . . . . . . . . . . . . . . . . . . . . . 105
14 3 9
5.2 Edge states at the dark side of the weak topological insulator
Bi Rh I probedbySTS . . . . . . . . . . . . . . . . . . . . . . . 109
14 3 9
5.2.1 Identification of the atomic and electronic structure of
thedifferentlayersinBi Rh I bySTM . . . . . . . . . . 109
14 3 9
5.2.2 Bias-dependent structural variations of the
morphologyofthe2DTIandspacerlayerinBi Rh I . 114
14 3 9
5.2.3 Probingtheedgestateatthestepedgeofthe2DTIlayer
inBi Rh I . . . . . . . . . . . . . . . . . . . . . . . . . . 122
14 3 9
5.2.4 Evidenceforthetopologicalnatureoftheedgestatein
Bi Rh I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
14 3 9
5.2.5 Absenceofanedgestateinthestructuralcloselyrelated
buttopologicallytrivialmaterialBi Pt I . . . . . . . . . 134
13 3 7
5.2.6 Computationaldetails . . . . . . . . . . . . . . . . . . . . 141
6 Summary 143
Bibliography 145
Publications 165
1 Introduction
In recent years, a new type of quantum matter has emerged in the field of
condensedmattersphysics,whichaddsafundamentalnewclassofmaterials
tothesofarbasicdistinctionbetweenconductorsandinsulators. However,
theclassificationintosystemswhichareabletoconductanelectricalcurrent
andsystemswhicharenot,isnotcomplete. Thediscoveryoftheintegerand
fractionalquantumHalleffectinthe1980’srevealedthatthereexistsystems
whichareinsulatinginthebulk,butnecessarilyexhibitagaplessedgestateat
theboundarieswiththeimportantcharacteristicthattheboundaryconduc-
tanceisarequirementofthebulkpropertiesofthesystem[1,2].Thesestates
havebeensuccessfullydeducedbytopologicalbandtheoryorevenmoreab-
stracttopologicalarguments,takingintoaccountconceptslikeBerryphases
andChernnumbers[3,4].
In the integer quantum Hall effect, a magnetic field is required in order
to exhibit the quantized Hall conductance at the boundaries, however very
recently, examples of topological phases with an insulating bulk and con-
ducting boundary states without external magnetic field have been discov-
eredandreferredtoastopologicalinsulators(TIs)[5,6,7,8,9,10,11]. This
newquantumstate,whichisalsoknownundertheterminologyofquantum
spinHallstate,isinvariantundertime-reversalsymmetryandexhibitsapair
of oppositely spin-polarized boundary states with spin-up and spin-down
propagating in opposite directions. The helical nature, i.e. the correlation
between the spin and the momentum of the edge states, is thereby due to
time-reversalsymmetryandthetopologicalcharacterofthebandgap,which
itselfiscausedbythestrongspin-orbit(SO)interactionpresentwithinthese
systems. In detail, the SO interaction modifies the energy gap between the
emptyandtheoccupiedstatesofinsulatorssothatsomeofthestateswhich
wereinitiallylocatedabovethegaparenowlyingbelowthegap.Analogous
totheconceptoftheMöbiusstripinmathematics,thispartialinversionofthe
bandgapcannotbesimplyunwoundwithoutclosingthegap, introducing
the notion of topology into these specific insulators. From this topological
pointofview,abandinsulatorwithapartiallyinvertedbandgapistopolog-
icallydistinctfromabandinsulatorwithatrivialbandgapwhichisreferred
to as non-trivial and trivial. The term topological here defines a bulk invari-
ant(aninteger)whichdifferentiatesbetweenthesedistinctinsulatingphases
and classifies them accordingly. In other words, the topological distinction
C. Pauly, Strong and Weak Topology Probed by Surface Science, MatWerk,
DOI 10.1007/978-3-658-11811-2_1, © Springer Fachmedien Wiesbaden 2015