finding and characterizing new topological...
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![Page 1: FINDING AND CHARACTERIZING NEW TOPOLOGICAL MATERIALStms17.dipc.org/lecture-notes/lecture-2-schoop.pdf · 2017-10-11 · FINDING AND CHARACTERIZING NEW TOPOLOGICAL MATERIALS LESLIE](https://reader033.vdocuments.us/reader033/viewer/2022042121/5e9b82d986a8e938807c4a41/html5/thumbnails/1.jpg)
Max Planck Institute for Solid State Research
FINDING AND CHARACTERIZING NEW
TOPOLOGICAL MATERIALS LESLIEMAREIKESCHOOP
TOPOLOGICALMATTERSCHOOL2017
DONOSTIA-SANSEBASTIAN
08/24/17
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Crystalchemistryandstructure
Electronicstructure ProperKes
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RECAP: WHAT TO WE NEED TO FIND A 3D DSM
• ChargeBalance• Highsymmetry
• “good”raKobetweenelectronegaKvityandspinorbitcoupling
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A CHEMIST’S PROBLEMS WITH KNOWN 3D DIRAC AND WEYL SEMIMETALS
• Toxic(arsenides)• AirsensiKve(Na3Bi)
• WTe2andZrTe5,bothnotstableinairwhenthin
• Verysmallrangeoflinearbands
• Nonearemadeofonlyearthabundantelements
Cd3As2
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HOW TO DEVELOP NEW MATERIALS
Theidea
Designasuitablematerial
Calculateelectronicstructure
Synthesizedesiredmaterial
CharacterizaKon
MeasureproperKes
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SYNTHESIS METHODS:
• Mostcommoncrystalgrowthmethods:
• Vaportransport(e.g.TaAs,ZrSiS)• Fluxgrowth(e.g.Cd3As2,Na3Bi,WTe2)
• Bridgmangrowth(e.g.Bi2Se3,Bi2Te3,BTS)
• FloaKngzone(e.g.MnSi)
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VAPOR TRANSPORT:
• WorksusuallywellformaterialscontainingS,Se,PorAs
• DependentontheabilitytoformvolaKleintermediateproductsthatgotothegasphase
• Famousexamples:
• TaAs,NbPetc
• ZrSiS
A(s) B(g) A(s) AB(g)
T2 T1Quartztube
Solidreactants
Gaseoustransportagent
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POSSIBLE TRANSPORT AGENTS
• I2:easytohandle,workswellforZr,Hf,NbandTacompounds
• Br2,aliblehardertohandlebutsomeKmesbeberresult
• Cl2nasty!ButsomeKmesnecessary(e.g.RuCl3)
• SeCl4orTeCl4:GoodsubsKtuteforCl2• NH4Cl(HClisacKvetransportagent)workswellforSnS2oroxysulfides
SeCl4àSe(g)+2Cl2(g)NH4ClàNH3(g)+HCl
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SEED GROWTH
• Vaportransportcanleadtoextremelylargesinglecrystals
• Ofenextremelypure
• Seedgrowthcanyieldevenlargercrystals
Panella,Trump,Marcus,McQueen,arXiv:1706.02411.
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LIMITATIONS OF VAPOR TRANSPORT:
Scien&ficReports5,ArKclenumber:12966(2015)
• Cd3As2:compeKngphases!
• Grownwithvaportransport:largecrystalsBUTRRRonlyabout8
• GrownfromFlux:RRR>4000
• Onlyfluxgrowncrystalsshowultrahighmobility!
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LIMITATIONS ON VAPOR TRANSPORT
• WTe2:
• MagnetoresistanceMUCHhigherifcrystalsaregrownfromTeflux
• ProbablybecauseTevacanciesformeasily
Ali,Schoop,Xiong,Flynn,Gibson,Hirschberger,Ong,Cava.EPL(EurophysicsLe6ers),110(6),p.67002.(2015)
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FLUX GROWTH
• Advantage:quenchonephase,excessofvolaKleelementpossible
• Disadvantage:centrifugingathighTcausedefects
• Famousexamples:
• Cd3As2,WTe2,ZrTe5Fe-basedsupercondcutors,Na3Bi
Centrifuga,onathightemperatures
FluxMethodQuartzwoolfilter
Liquidmetalorsalt
xtal
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POSSIBLE FLUXES
• LowmelKngpointelements:In,Sn,Pb,Sb,Bi,Te
• Selffluxorforeignfluxpossible
• Studyphasediagrams!
• Saltsandoxides
Saltandoxidefluxes
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BRIDGMAN METHOD
• Veryeasy:justheatunKleverythingmeltsandcoolveryslowlyfromoneendtotheotherofthecontainer
• OfenthebestsoluKonbutworksonlyforspecialphases
• Famousexamples:Bi2Se3andothertetradymites
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VERIFYING THE BAND STRUCTURE
• Yousuccessfullygrewalargeenoughcrystal!YayyJ
• NextQuesKon:doesitcleave???
• ARPESwillbedoneinUHVandneedacleansurface!!
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HOW TO EXPERIMENTALLY VERIFY THE ELECTRONIC STRUCTURE
• UseAngleResolvedPhotoelectronSpectroscopytotakeanimageofthebandstructure
• SurfacesensiKve!• Largesinglecrystals(min.1mm2)thatcanbecleavedinUHVneeded
Photonsource�ω
Releasedphotoelectrons
SortsphotoelectronsbyEkinandemissionangleθ
EB=�ω-ϕ-Ekin
2DCCDdetector
"↓|| = √2& /ℏ √(↓")* sin +
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THE PHOTOELECTRIC EFFECT
ħω
Ekin
ħω
Crystal
Vacuum
e-
1
2
3
h
The three-step-model describes the photoelectric effect: 1. Excitation of the electron 2. Propagation to the surface (most limiting factor) 3. Transition into the vacuum
One-step-model is more “correct”, but less intuitive…
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THE PHOTOELECTRIC EFFECT -THE „UNIVERSAL“ CURVE
ToolowenergytoexceedworkfuncKon
ToosmallBZandSmallcrosssecKon(photonsdon’treallykickelectronsout)
OpKmalrangeforARPES
LimiKngfactoristhatelectronscanleavethecrystals,nothowdeepphotonscanenter
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ENERGY CONVERSION:
Ei =�ω-Φ-Ekin
withEkin: kinetic energy of the emitted electronΦ: work functionEi: initial state energy(negative binding energy)ħω: photon energy
The photoelectron has a certain momentum and kinetic energy: The energy reference for the binding energy is the Fermi level.
MeasuredkineKcEnergyWanted:bindingenergy
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MOMENTUM CONVERSION:
θThe photoelectron has a certain momentum and kinetic energy: Only the momentum component parallel to the surface is conserved.
Adjust:exitangle+Wanted:momentum(K||)
"↓|| = √2& /ℏ √(↓")* sin +
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ENERGY DISTRIBUTION CURVES (EDCS)
Fit of an EDC: • Lorentz curve • Fermi-Dirac Function • Shirley Background
Peak (mostly Lorentzian)
Fermi level
Shirley Background
Normal emission is an important position as here the Γ-points are located.
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THE IMAGE WE GET OUT OF THE MACHINE
Individual EDCs ħω=700eV
Analyzer usually contains a CCD camera nowadays, which allows to measure EDCs as a function of slit angle showing the band structure.
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MEASURING THE FULL BZ
ħω=700eV θ=-2° ħω=700eV θ=5°
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PLOTTING ALONG DIFFERENT DIRECTIONS
ħω=700eV slit angle=const
Cut along the slit angle
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FERMI SURFACE PLOT
EF
ħω=700eV
Constant energy plot - FS
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K SPACE CONVERSION
ħω=700eV
Constant energy plot - FS
(α)
Γ(0/0)
"↓, = √2& /ℏ √(↓")* sin +
(↓- = (↓. − (↓")*
"↓/ = √2& /ℏ √(↓")* sin α cos+
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K SPACE CONVERSION
≈0.512
Important: Constant angle slices are not constant kǁ slices
→interpolation between data points necessary Constant energy slices remain meaningful
"↓, = √2& /ℏ √(↓")* sin +
"↓/ = √2& /ℏ √(↓")* sin α cos+
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FINALIZING YOUR DATA ANALYSIS
Usuallykxandkyaredefinedalonghighsymmetrylines→rotatedatacubeaferconversion
Γ X
M
("↓/ ¦"↓, )=(█cosφ &− sin φ @sin φ &cosφ )("↓/ ¦"↓, )
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ARPES DATA ANALYSIS - SUMMARY Steps:1. Findα-offset,θ-offset(Γshouldbeat(0/0))andEF
§ findΓthroughsymmetryandsamplegeometry§ determineEFbyfi~ngtoFermi-DiracfuncKon
2. UseconversionequaKons
3. Rotatedatacubetoalignhighsymmetrylinesalongkxorky
"↓, = √2& /ℏ √(↓")* sin +
(↓- = (↓. − (↓")*
"↓/ = √2& /ℏ √(↓")* sin α cos+
("↓/ ¦"↓, )=(█cosφ &− sin φ @sin φ &cosφ )("↓/ ¦"↓, )
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SOME EXAMPLES OF THE “FULL LOOP”
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WHERE TO LOOK?
• RoaldHoffmannandWolfgangTremel:PhasetransiKonsinsquarenetcompounds
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ZrSiS WOULD FULFILL ALL MY REQUIREMENTS
• Nontoxic• Onlyearthabundantelements
• Verystableinairandwater• Shouldbecleavable
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ZINTL PHASES: COUNT ELECTRONS TO FIND NUMBER OF BONDS
• NumberofbondsinPolyanions:
• b(xx)=8(or18)-VEC(x)
4+4+6=1414perSib(Si-Si)=18-14=4
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BULK BAND STRUCTURE OF ZrSiS
• Hugerangeoflineardispersion
• ManyDiracconesaroundtheFermilevel
• Linenode!• GetgappedbySOC,butSOCissmall
Schoop,Ali,Straßer,Topp,Duppel,Parkin,Lotsch,Ast,Nat.Comm.,7,11696(2016)
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MAKING THE SAMPLE
• Largecrystalsgrownwithvaportransport• Cleaveswell
1mm
Zr+Si+SI2 ZrSiS
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CHARACTERIZING THE SAMPLE
1)singlecrystaldiffracKon:Rvalueof2%
2)electrondiffracKon
3)HighresoluKonTEM
4)Chemicalanalysis
5)STMtopography
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ARPES MEASUREMENTS
• Surfacestatesappear
• Largelinerdispersionvisible
Schoop,Ali,Strasser,Topp,Duppel,Parkin,Lotsch,Ast,Nat.Comm.,7,11696(2016)
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SURFACE STATES?
• Calculateaslab• PerfectmatchbetweenDFTandARPES
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GOING BEYOND ZrSiS
• ThefamilyofMXZcompoundswiththesamestructurethanZrSiShostsmanymoreDiracmaterials
• Nearly200morecompoundstoinvesKgate
• Hightunability,lotsofroomforimprovement!
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REALIZING NON-SYMMORPHIC SEMIMETALS
• Requireoddelectroncount(performulaunit)
• Chemicallyunstable!
“convenKonalDSM” “non-symmorphicDSM”
3*2+2*5=168perAs
3*1+5=8
Cd3As2
Na3Bi
Trivialinsulator(evene-/site)
Non-trivialDiracmetal(odde-/site)
Gibsonetal.PhysicalReviewB91(20),205128(2015)
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HOW TO TACKLE THIS CHALLENGE EXPERIMENTALLY?
Twosteps:
(a)CanweexperimentallyverifythatbanddegeneraciesforcedbyNS-SymmetryexistbelowtheFermilevel?
(b)Aferfindingamodelcompound,canwemovethisdegeneracytotheFermilevel?
(a)Realizethiscase:
(b)ShifFermilevel
Trivialinsulator(evene-/site)
Non-trivialDiracmetal(odde-/site)
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STEP A: ZrSiS
• SpacegroupP4/nmm
Xpoint
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MOVE NON-SYMMORPHIC CROSSING TO THE FERMI LEVEL?
• FamilyofMZXcompounds
• Isoelectronic
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STEP B: ZrSiTe
20160111zrsite_125ev_v2
ZrSiTe:• Non-symmorphicbanddegeneracyattheFermilevel
ZrSiS
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BULK BAND STRUCTURE OF ZrSiTe
Topp,Lippmann,Varykhalov,Duppel,Lotsch,Ast,Schoop,NewJPhys.,18,125014(2016)
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ZrSiTe CRYSTAL GROWTH
• Hightemperaturephase!Quenchsamples• CrystalsareairsensiKve• Cleaveswithscotchtape
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ARPES ON ZrSiTe
Topp,Lippmann,Varykhalov,Duppel,Lotsch,Ast,Schoop,NewJPhys.,18,125014(2016)
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ARPES ON ZrSiTe
Potassiumonsurface
Topp,Lippmann,Varykhalov,Duppel,Lotsch,Ast,Schoop,NewJPhys.,18,125014(2016)
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CAN WE USE CHEMISTRY IT MAKE WEYL SEMIMETALS?
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WHAT ABOUT THE RARE EARTH COMPOUNDS? LnSbTe
DotheLnSbTephasesordermagneKcally?
LaSbTe
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CRYSTAL GROWTH OF CeSbTe
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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MAGNETIC PROPERTIES OF CeSbTe
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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MAGNETIC PROPERTIES OF CeSbTe
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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ANTIFERROMAGNETIC STRUCTURE OF CeSbTe
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)
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MAGNETIC PHASE DIAGRAM OF CeSbTe
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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GROUP THEORY ANALYSIS
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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CeSbTe – A MODEL SYSTEM TO UNDERSTAND MAGNETIC NON-SYMMORPHIC MATERIALS?
Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)arXiv:1707.03408
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APRES CONFIRMS BAND STRUCTURE OF PARAMAGNETIC PHASE
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SUMMARY
• SquarenetsareaveryrichplaygroundforDirac/Weylphysics!
Linerbands Tunetheelectronicstrucutre MakeitmagneKc
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THANK YOU! • Be~naLotsch
• ViolaDuppel
• ChrisKanAst
• CarolaStrasser
• AndreasTopp
• JudithLippmann
• AndreasRost
• JudithLippmann
• QingyuHe
• LihuiZhu
• RaquelQueiroz
• AndreyVarykhalov(Bessy)
• SteffenWiedmann(HMFL)
• NigelHussey(HMFL)
• LukasMuechler(Princeton)
• MaiaVergniory(DIPC)