finding and characterizing new topological...

Max Planck Institute for Solid State Research

FINDING AND CHARACTERIZING NEW

TOPOLOGICAL MATERIALS LESLIEMAREIKESCHOOP

TOPOLOGICALMATTERSCHOOL2017

DONOSTIA-SANSEBASTIAN

08/24/17

Crystalchemistryandstructure

Electronicstructure ProperKes

RECAP: WHAT TO WE NEED TO FIND A 3D DSM

•  ChargeBalance•  Highsymmetry

•  “good”raKobetweenelectronegaKvityandspinorbitcoupling

A CHEMIST’S PROBLEMS WITH KNOWN 3D DIRAC AND WEYL SEMIMETALS

•  Toxic(arsenides)•  AirsensiKve(Na3Bi)

•  WTe2andZrTe5,bothnotstableinairwhenthin

•  Verysmallrangeoflinearbands

•  Nonearemadeofonlyearthabundantelements

Cd3As2

HOW TO DEVELOP NEW MATERIALS

Theidea

Designasuitablematerial

Calculateelectronicstructure

Synthesizedesiredmaterial

CharacterizaKon

MeasureproperKes

SYNTHESIS METHODS:

•  Mostcommoncrystalgrowthmethods:

•  Vaportransport(e.g.TaAs,ZrSiS)•  Fluxgrowth(e.g.Cd3As2,Na3Bi,WTe2)

•  Bridgmangrowth(e.g.Bi2Se3,Bi2Te3,BTS)

•  FloaKngzone(e.g.MnSi)

VAPOR TRANSPORT:

•  WorksusuallywellformaterialscontainingS,Se,PorAs

•  DependentontheabilitytoformvolaKleintermediateproductsthatgotothegasphase

•  Famousexamples:

•  TaAs,NbPetc

•  ZrSiS

A(s) B(g) A(s) AB(g)

T2 T1Quartztube

Solidreactants

Gaseoustransportagent

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

SEED GROWTH

•  Vaportransportcanleadtoextremelylargesinglecrystals

•  Ofenextremelypure

•  Seedgrowthcanyieldevenlargercrystals

Panella,Trump,Marcus,McQueen,arXiv:1706.02411.

LIMITATIONS OF VAPOR TRANSPORT:

Scien&ficReports5,ArKclenumber:12966(2015)

•  Cd3As2:compeKngphases!

•  Grownwithvaportransport:largecrystalsBUTRRRonlyabout8

•  GrownfromFlux:RRR>4000

•  Onlyfluxgrowncrystalsshowultrahighmobility!

LIMITATIONS ON VAPOR TRANSPORT

•  WTe2:

•  MagnetoresistanceMUCHhigherifcrystalsaregrownfromTeflux

•  ProbablybecauseTevacanciesformeasily

Ali,Schoop,Xiong,Flynn,Gibson,Hirschberger,Ong,Cava.EPL(EurophysicsLe6ers),110(6),p.67002.(2015)

FLUX GROWTH

•  Advantage:quenchonephase,excessofvolaKleelementpossible

•  Disadvantage:centrifugingathighTcausedefects

•  Famousexamples:

•  Cd3As2,WTe2,ZrTe5Fe-basedsupercondcutors,Na3Bi

Centrifuga,onathightemperatures

FluxMethodQuartzwoolfilter

Liquidmetalorsalt

xtal

POSSIBLE FLUXES

•  LowmelKngpointelements:In,Sn,Pb,Sb,Bi,Te

•  Selffluxorforeignfluxpossible

•  Studyphasediagrams!

•  Saltsandoxides

Saltandoxidefluxes

BRIDGMAN METHOD

•  Veryeasy:justheatunKleverythingmeltsandcoolveryslowlyfromoneendtotheotherofthecontainer

•  OfenthebestsoluKonbutworksonlyforspecialphases

•  Famousexamples:Bi2Se3andothertetradymites

VERIFYING THE BAND STRUCTURE

•  Yousuccessfullygrewalargeenoughcrystal!YayyJ

•  NextQuesKon:doesitcleave???

•  ARPESwillbedoneinUHVandneedacleansurface!!

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 + 

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…

THE PHOTOELECTRIC EFFECT -THE „UNIVERSAL“ CURVE

ToolowenergytoexceedworkfuncKon

ToosmallBZandSmallcrosssecKon(photonsdon’treallykickelectronsout)

OpKmalrangeforARPES

LimiKngfactoristhatelectronscanleavethecrystals,nothowdeepphotonscanenter

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

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 + 

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.

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.

MEASURING THE FULL BZ

ħω=700eV θ=-2° ħω=700eV θ=5°

PLOTTING ALONG DIFFERENT DIRECTIONS

ħω=700eV slit angle=const

Cut along the slit angle

FERMI SURFACE PLOT

EF

ħω=700eV

Constant energy plot - FS

K SPACE CONVERSION

ħω=700eV

Constant energy plot - FS

(α)

Γ(0/0)

"↓, = √2& /ℏ √(↓")*  sin + 

(↓- = (↓. − (↓")* 

"↓/ = √2& /ℏ √(↓")*  sin α cos+ 

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+ 

FINALIZING YOUR DATA ANALYSIS

Usuallykxandkyaredefinedalonghighsymmetrylines→rotatedatacubeaferconversion

Γ X

M

("↓/ ¦"↓,  )=(█cosφ &− sin φ @sin φ &cosφ  )("↓/ ¦"↓,  )

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  )("↓/ ¦"↓,  )

SOME EXAMPLES OF THE “FULL LOOP”

WHERE TO LOOK?

•  RoaldHoffmannandWolfgangTremel:PhasetransiKonsinsquarenetcompounds

ZrSiS WOULD FULFILL ALL MY REQUIREMENTS

•  Nontoxic•  Onlyearthabundantelements

•  Verystableinairandwater•  Shouldbecleavable

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

BULK BAND STRUCTURE OF ZrSiS

•  Hugerangeoflineardispersion

•  ManyDiracconesaroundtheFermilevel

•  Linenode!•  GetgappedbySOC,butSOCissmall

Schoop,Ali,Straßer,Topp,Duppel,Parkin,Lotsch,Ast,Nat.Comm.,7,11696(2016)

MAKING THE SAMPLE

•  Largecrystalsgrownwithvaportransport•  Cleaveswell

1mm

Zr+Si+SI2 ZrSiS

CHARACTERIZING THE SAMPLE

1)singlecrystaldiffracKon:Rvalueof2%

2)electrondiffracKon

3)HighresoluKonTEM

4)Chemicalanalysis

5)STMtopography

ARPES MEASUREMENTS

•  Surfacestatesappear

•  Largelinerdispersionvisible

Schoop,Ali,Strasser,Topp,Duppel,Parkin,Lotsch,Ast,Nat.Comm.,7,11696(2016)

SURFACE STATES?

•  Calculateaslab•  PerfectmatchbetweenDFTandARPES

GOING BEYOND ZrSiS

•  ThefamilyofMXZcompoundswiththesamestructurethanZrSiShostsmanymoreDiracmaterials

•  Nearly200morecompoundstoinvesKgate

•  Hightunability,lotsofroomforimprovement!

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)

HOW TO TACKLE THIS CHALLENGE EXPERIMENTALLY?

Twosteps:

(a)CanweexperimentallyverifythatbanddegeneraciesforcedbyNS-SymmetryexistbelowtheFermilevel?

(b)Aferfindingamodelcompound,canwemovethisdegeneracytotheFermilevel?

(a)Realizethiscase:

(b)ShifFermilevel

Trivialinsulator(evene-/site)

Non-trivialDiracmetal(odde-/site)

STEP A: ZrSiS

•  SpacegroupP4/nmm

Xpoint

MOVE NON-SYMMORPHIC CROSSING TO THE FERMI LEVEL?

•  FamilyofMZXcompounds

•  Isoelectronic

STEP B: ZrSiTe

20160111zrsite_125ev_v2

ZrSiTe:•  Non-symmorphicbanddegeneracyattheFermilevel

ZrSiS

BULK BAND STRUCTURE OF ZrSiTe

Topp,Lippmann,Varykhalov,Duppel,Lotsch,Ast,Schoop,NewJPhys.,18,125014(2016)

ZrSiTe CRYSTAL GROWTH

•  Hightemperaturephase!Quenchsamples•  CrystalsareairsensiKve•  Cleaveswithscotchtape

ARPES ON ZrSiTe


ARPES ON ZrSiTe

Potassiumonsurface


CAN WE USE CHEMISTRY IT MAKE WEYL SEMIMETALS?

WHAT ABOUT THE RARE EARTH COMPOUNDS? LnSbTe

DotheLnSbTephasesordermagneKcally?

LaSbTe

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

MAGNETIC PROPERTIES OF CeSbTe


ANTIFERROMAGNETIC STRUCTURE OF CeSbTe

Schoop,Topp,Lippmann,Orlandi,Muechler,Vergniory,Sun,Rost,Duppel,Krivenkov,Sheoran,Manuel,Varykhalov,Yan,Kremer,Ast,Lotschsubmi6ed(2017)

MAGNETIC PHASE DIAGRAM OF CeSbTe


GROUP THEORY ANALYSIS


CeSbTe – A MODEL SYSTEM TO UNDERSTAND MAGNETIC NON-SYMMORPHIC MATERIALS?


APRES CONFIRMS BAND STRUCTURE OF PARAMAGNETIC PHASE

SUMMARY

•  SquarenetsareaveryrichplaygroundforDirac/Weylphysics!

Linerbands Tunetheelectronicstrucutre MakeitmagneKc

THANK YOU! •  Be~naLotsch

•  ViolaDuppel

•  ChrisKanAst

•  CarolaStrasser

•  AndreasTopp

•  JudithLippmann

•  AndreasRost

•  JudithLippmann

•  QingyuHe

•  LihuiZhu

•  RaquelQueiroz

•  AndreyVarykhalov(Bessy)

•  SteffenWiedmann(HMFL)

•  NigelHussey(HMFL)

•  LukasMuechler(Princeton)

•  MaiaVergniory(DIPC)

finding and characterizing new topological...

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