vanishhosting24

ARTICLESignaturesofatime-reversalsymmetricWeylsemimetalwithonlyfourWeylpointsIlyaBelopolski1,PengYu2,DanielS.
Sanchez1,YukiakiIshida3,Tay-RongChang4,5,SongtianS.
Zhang1,Su-YangXu1,HaoZheng1,GuoqingChang6,7,GuangBian1,8,Horng-TayJeng4,9,TakeshiKondo3,HsinLin6,7,ZhengLiu2,10,11,ShikShin3&M.
ZahidHasan1,12ThroughintenseresearchonWeylsemimetalsduringthepastfewyears,wehavecometoappreciatethattypicalWeylsemimetalshostmanyWeylpoints.
Nonetheless,theminimumnonzeronumberofWeylpointsallowedinatime-reversalinvariantWeylsemimetalisfour.
Realizingsuchasystemisoffundamentalinterestandmaysimplifytransportexperiments.
Recently,itwaspredictedthatTaIrTe4realizesaminimalWeylsemimetal.
However,theWeylpointsandFermiarcsliveentirelyabovetheFermilevel,makingtheminaccessibletoconventionalangle-resolvedphotoemissionspectroscopy(ARPES).
Here,weusepump-probeARPEStodirectlyaccessthebandstructureabovetheFermilevelinTaIrTe4.
WeobservesignaturesofWeylpointsandtopologicalFermiarcs.
Combinedwithabinitiocalculation,ourresultsshowthatTaIrTe4isaWeylsemimetalwiththeminimumnumberoffourWeylpoints.
OurworkprovidesasimplerplatformforaccessingexotictransportphenomenaarisinginWeylsemimetals.
DOI:10.
1038/s41467-017-00938-1OPEN1LaboratoryforTopologicalQuantumMatterandSpectroscopy(B7),DepartmentofPhysics,PrincetonUniversity,Princeton,NJ08544,USA.
2CentreforProgrammableMaterials,SchoolofMaterialsScienceandEngineering,NanyangTechnologicalUniversity,Singapore639798,Singapore.
3InstituteforSolidStatePhysics(ISSP),UniversityofTokyo,Kashiwa-no-ha,Kashiwa,Chiba277-8581,Japan.
4DepartmentofPhysics,NationalTsingHuaUniversity,Hsinchu30013,Taiwan.
5DepartmentofPhysics,NationalChengKungUniversity,Tainan701,Taiwan.
6CentreforAdvanced2DMaterialsandGrapheneResearchCentre,NationalUniversityofSingapore,6ScienceDrive2,Singapore117546,Singapore.
7DepartmentofPhysics,NationalUniversityofSingapore,2ScienceDrive3,Singapore117542,Singapore.
8DepartmentofPhysicsandAstronomy,UniversityofMissouri,Columbia,MO65211,USA.
9InstituteofPhysics,AcademiaSinica,Taipei11529,Taiwan.
10NOVITAS,NanoelectronicsCentreofExcellence,SchoolofElectricalandElectronicEngineering,NanyangTechnologicalUniversity,Singapore639798,Singapore.
11CINTRACNRS/NTU/THALES,UMI3288,ResearchTechnoPlaza,50NanyangDrive,BorderXBlock,Level6,Singapore637553,Singapore.
12PrincetonInstituteforScienceandTechnologyofMaterials,PrincetonUniversity,Princeton,NJ08544,USA.
IlyaBelopolskiandPengYucontributedequallytothiswork.
CorrespondenceandrequestsformaterialsshouldbeaddressedtoI.
B.
(email:ilyab@princeton.
edu)ortoM.
Z.
H.
(email:mzhasan@princeton.
edu)NATURECOMMUNICATIONS|(2017)8:942|DOI:10.
1038/s41467-017-00938-1|www.
nature.
com/naturecommunications1AWeylsemimetalisacrystalwhichhostsemergentWeylfermionsaselectronicquasiparticles.
Inanelectronicbandstructure,theseWeylfermionscorrespondtoacci-dentaldegeneracies,orWeylpoints,betweentwobands1–5.
Itiswell-understoodthatWeylpointscanonlyariseifamaterialbreakseitherspatialinversionsymmetry,I,ortime-reversalsymmetry,T6–9.
Atthesametime,inaWeylsemimetal,sym-metriesofthesystemtendtoproducecopiesofWeylpointsintheBrillouinzone.
Asaresult,typicalWeylsemimetalshostaproliferationofWeylpoints.
Forinstance,therstWeylsemi-metalsobservedinexperiment,TaAsanditsisoelectroniccou-sins,haveanIbreakingcrystalstructure,whichgivesrisetoabandstructurehosting24WeylpointsdistributedthroughoutthebulkBrillouinzone10–17.
However,mostoftheseWeylpointscanberelatedtooneanotherbytheremainingsymmetriesofTaAs,namelytwomirrorsymmetries,C4rotationsymmetryandT.
IntheMoxW1xTe2series,whichhasrecentlybeenunderintensivetheoreticalandexperimentalstudyasaWeylsemimetalwithstronglyLorentz-violating,orTypeII,Weylfermions,mirrorsymmetryandTrelatesubsetsoftheeightWeylpoints18–25.
Asanotherexample,accordingtocalculation,theWeylsemimetalcandidateSrSi2hostsnofewerthan108Weylpoints,copiedinsetsof18bythreeC4rotationsymmetries26.
However,aswereviewbelow,itiswell-knownthattheminimalnonzeronumberofWeylpointsallowedis4foraTinvariantWeylsemimetal.
RealizingsuchaminimalWeylsemimetalisnotonlyoffunda-mentalinterest,butisalsopracticallyimportant,becauseasystemwithfewerWeylpointsmayexhibitsimplerpropertiesintrans-portandbemoresuitablefordeviceapplications.
Recently,TaIrTe4waspredictedtobeaWeylsemimetalwithonlyfourWeylpoints27.
ItwasfurthernotedthattheWeylpointsareassociatedwithTypeIIWeylfermions,providingonlythesecondexampleofaTypeIIWeylsemimetalaftertheMoxW1xTe2series18.
Moreover,theWeylpointsarewell-separatedinmomentumspace,withsubstantiallylargertopologicalFermiarcsasafractionofthesizeofthesurfaceBrillouinzonethanotherknownWeylsemimetals.
Lastly,TaIrTe4hasalayeredcrystalstructure,whichmaymakeiteasiertocarryouttransportexperimentsanddevelopdeviceapplications.
AllofthesedesirablepropertieshavemotivatedconsiderableresearchinterestinTaIrTe4.
Atthesametime,onecrucialchallengeisthattheWeylpointsandtopologicalFermiarcsarepredictedtoliveentirelyabovetheFermilevelinTaIrTe4,sothattheyareinaccessibletoconventionalangle-resolvedphotoemissionspectroscopy(ARPES).
Here,weobservesignaturesofWeylpointsandtopologicalFermiarcsinTaIrTe4,realizingtherstminimalTinvariantWeylsemimetal.
Werstbrieyreiterateawell-knowntheore-ticalargumentthattheminimumnumberofWeylpointsforaTinvariantWeylsemimetalisfour.
Then,wepresentabinitiocalculationsshowinganearlyidealcongurationofWeylpointsandFermiarcsinTaIrTe4.
Next,weusepump-probeARPEStodirectlyaccessthebandstructureofTaIrTe4abovetheFermilevelinexperiment.
Wereporttheobservationofsignaturesof11.
0defabc0.
100.
050.
00–0.
1e–h+0.
0FermiarcEFky(–1)0.
1TYRUXX–S–Y–SZ(001)0.
5–0.
5–1.
0XSYSRUZRTZ0.
0ΓΓΓΓΓ–ΓΓ+11TaIrTe+1zxykzkz=0kykykxkzkykykxkxkxEB(eV)EB(eV)Fig.
1ConstraintsonWeylpointsinTsymmetricsystems.
aIllustrationoftheminimalnumberofWeylpointsinaTinvariantWeylsemimetal.
TheblueandredcirclesandconesrepresentWeylpointsandWeylconeswith±1chiralchargeatgenerick-points.
InaTinvariantWeylsemimetal,theminimalnumberofWeylpointsisfourbecauseTsymmetrysendsaWeylpointofagivenchiralchargeatktoaWeylpointofthesamechiralchargeatk(orangearrow).
Topreservenetzerochiralcharge,fourWeylpointsareneeded.
bThecrystalstructureofTaIrTe4islayered,inspacegroup31,whichbreaksinversionsymmetry.
cThebulkBrillouinzone(BZ)and(001)surfaceBZofTaIrTe4withhigh-symmetrypointsmarkedinred.
dTheelectronicbandstructureofTaIrTe4alonghigh-symmetrylines.
ThereisabandcrossingintheregionnearΓ,withWeylpointsoffΓS(bluebox).
eCartoonillustrationoftheconstant-energycontouratEB=EWandkz=0,withbulkelectronandholepocketswhichintersecttoformWeylpoints.
AdetailedcalculationshowsthatthereareintotalfourTypeIIWeylpoints(blueandredcircles)27.
fEnergy-dispersioncalculationalongapairofWeylpointsinthekydirection,markedbytheorangelineine.
TheWeylpointsandFermiarcsliveat~0.
1eVaboveEF,requiringtheuseofpump-probeARPEStodirectlyaccesstheunoccupiedbandstructuretodemonstrateaWeylsemimetalARTICLENATURECOMMUNICATIONS|DOI:10.
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Combinedwithabinitiocalculations,ourresultsdemonstratethatTaIrTe4hasfourWeylpoints.
WeconcludethatTaIrTe4canbeviewedasaminimalWeylsemimetal,withthesimplestcongurationofWeylpointsallowedinaTinvariantcrystal.
ResultsMinimumnumberofWeylpointsundertime-reversalsym-metry.
Werstreiteratewell-knownargumentsthatfouristheminimumnumberofWeylpointsallowedinaTinvariantWeylsemimetal.
AWeylpointisassociatedwithachiralcharge,directlyrelatedtothechiralityoftheassociatedemergentWeylfermion.
ItcanbeshownthatforanygivenbandthesumofallchiralchargesintheBrillouinzoneiszero.
Further,underTaWeylpointofagivenchiralchargeatkismappedtoanotherWeylpointofthesamechiralchargeatk.
ThisoperationofTonachiralchargeisillustratedinFig.
1aontheblueWeylpointswith+1chiralcharge(thesamearrowappliesfortheredWeylpointsbutisnotdrawnexplicitly).
Now,ifanIbreakingWeylsemimetalhasnoadditionalsymmetrieswhichproducecopiesofWeylpoints,thentheminimumnumberofWeylpointsisxedbyTsymmetryandtherequirementthattotalchiralchargevanish.
Inthesimplestcase,TwillproducetwocopiesofWeylpointsofchiralcharge+1,asshowninFig.
1a.
Tobalancetheseout,thesystemmusthavetwochiralchargesof1,alsorelatedbyT.
Inthisway,theminimumnumberofWeylpointsinaTinvariantWeylsemimetalisfour.
ThissimplescenarioisrealizedinTaIrTe4.
ThecrystalstructureofTaIrTe4isdescribedbyspacegroup31(Pmn21),latticeconstantsa=3.
77,b=12.
421,andc=13.
184,withlayeredcrystalstructure,seeFig.
1b.
WenotethatTaIrTe4takesthesamespacegroupasMoxW1xTe2,buthasaunitcelldoubledalongb.
TostudywheretheWeylpointsshowupinTaIrTe4wepresenttheelectronicbandstructurealongvarioushigh-symmetrydirections,seeBrillouinzoneandabinitiocalculationinFig.
1c,d.
EnclosedbytherectangularboxalongΓSisacrossingregionbetweenthebulkconductionandvalencebandsthatgivesrisetoWeylpoints.
AmoredetailedcalculationshowsthattheWeylpointshavetiltedover,orTypeII,WeylconesandthattheyliveabovetheFermilevel,EFatkz=027.
AcartoonschematicoftheresultingconstantenergycontourattheenergyoftheWeylpoints,EB=EW,isshowninFig.
1e.
TheelectronandholepocketsformTypeIIWeylconeswheretheytouch(redandbluemarks).
Inthisway,TaIrTe4hasfourWeylpoints,theminimalnumberallowedinanIbreakingWeylsemimetal.
TheoverallelectronicstructureofTaIrTe4nearEFissimilartoMoxW1xTe2,butwenotethattheroleoftheelectronandholepocketsisreversedinTaIrTe4relativetoMoxW1xTe2.
Also,MoxW1xTe2haseightWeylpoints,soitisnotminimal,andwewillseethatTaIrTe4alsohostslargerFermiarcsurfacestatesthanMoxW1xTe2.
TostudytheexpectedFermiarcsinTaIrTe4,wepresentanenergy-dispersioncutalongapairofprojectedWeylpointsalongky,Fig.
1f.
WeclearlyobservealargesingleFermiarcsurfacestateat~0.
1eVabovetheFermilevelthatis~0.
251longandconnectingapairof±1chiralchargedWeylpointsalongky.
Inthisway,TaIrTe4providesaminimalWeylsemimetalwithlargeFermiarcs.
LiketheWeylpoints,theFermiarcslivewellabovetheFermilevel,makingtheminac-cessibletoconventionalARPES.
UnoccupiedbandstructureofTaIrTe4bypump-probeARPES.
Next,weusepump-probeARPEStodirectlyaccesstheunoccu-piedbandstructureofTaIrTe4uptoEB>0.
2eVandwendexcellentagreementwithcalculation.
Inourexperiment,weusea1.
48eVpumplaserpulsetoexciteelectronsintolow-lyingstates–0.
2–0.
10.
00.
10.
20.
20.
0–0.
23(a)3(c)3(b)S1(a)2(a)2(b)2(c)EB=EF–0.
10.
00.
1–0.
10.
00.
1–0.
3–0.
2–0.
10.
00.
10.
2EB(eV)–0.
10.
00.
10.
10.
0–0.
11234560.
10.
0–0.
1ky~0.
07–1ky~0.
07–10.
10.
0–0.
1ky~0.
035–10.
10.
0–0.
10.
20.
10.
0–0.
1–0.
2ky~0–1ky=0.
0–1ky=0.
035–1ky=0.
07–1kx(–1)kx(–1)kx(–1)kx(–1)kx(–1)kx(–1)ky(–1)kx(–1)kx(–1)abcdefghEB(eV)Fig.
2UnoccupiedelectronicstructureofTaIrTe4.
a–cPump-probeARPESdispersionmapsofTaIrTe4,showingdispersionaboveEFatxedkynearΓ.
dSameascbutwithkeyfeaturesmarked.
e,fAbinitiocalculationofTaIrTe4.
Thedataiscapturedwellbycalculation,butthesampleappearstobeholedopedby~50meV,comparingthegreenandorangearrowsind,g.
hCalculationofthenominalFermisurface,showingweakdispersionalongkynearΓ,consistentwiththedata.
AllcutsinFigs.
2and3andSupplementaryFig.
1aremarked(solidanddashedlines)NATURECOMMUNICATIONS|DOI:10.
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92eVprobelaserpulsetoperformphotoemission28.
WestudyEBkxcutsnearΓ,Fig.
2a–c,withkeyfeaturesmarkedbyguidestotheeyeinFig.
2d.
AbovetheFermilevel,weseeacrossing-likefeaturenearEB~0.
15eV,labeled1,andtwoelectron-likebands,2and3,extendingoutaboveEF.
BelowtheFermilevel,weobserveageneralhole-likestructureconsistingofthreebands,labeled4–6.
AsweshiftkyoffΓ,wendlittlechangeinthespectrum,suggestingthatthebandstructureisratheratalongkynearΓ.
However,wecanobservethatband4movesdownwardinenergyandbecomesmoreintensewithincreasingky.
WendanexcellentmatchbetweenourARPESdataandabinitiocalculation,Fig.
2e–g.
Specically,weidentifythesamecrossing-likefeature(greenarrow)andtopofband4(orangearrow).
Wecanalsotrackband4inkyincalculationandwendthatthebandmovesdownandbecomesbrighteraskyincreases,inexcellentagreementwiththedata.
Theelectron-likestructureofbands2and3andthehole-likestruc-tureofbands5and6arealsobothcapturedwellbythecalcu-lation.
Crucially,however,wenoticeashiftinenergybetweenexperimentandtheory,showingthatthesampleishole-dopedby~0.
05eV.
Lastly,weplotaconstantenergykxkycutatEB=EF,whereweseeagainthatthereislittledispersionalongkynearΓ,+1–1kyEBIntensity(arb.
units)–0.
10.
00.
1–0.
2–0.
10.
00.
10.
2123Intensity(arb.
units)0.
20.
10.
0–0.
1S1(a)3(c)3(b)3(a)0.
20.
10.
0–0.
1123546kx~kW+0.
017–1kx~kW+0.
034–100.
2–0.
10.
00.
10.
2kx~kWkx~kWabcedfijkhgEB(eV)EB(eV)EB(eV)EB(eV)0.
10.
0–0.
10.
10.
0–0.
10.
10.
0–0.
10.
10.
0–0.
1ky(–1)ky(–1)ky(–1)ky(–1)0.
10.
0–0.
10.
10.
0–0.
10.
10.
0–0.
1ky(–1)ky(–1)ky(–1)ky(–1)0.
10.
0–0.
1ky(–1)kx=0.
19–1kx=0.
206–1kx=kW=0.
2–1Fig.
3WeylpointsandFermiarcsabovetheFermilevelinTaIrTe4.
a–cPumpprobeARPESspectraofTaIrTe4,showingdispersionaboveEFatxedkxexpectedtobeneartheWeylpoints.
dSamespectrumasabutwithkeyfeaturesmarked.
TheWeylconecandidatesarelabeled1and2,theFermiarccandidateislabeled3.
eEnergydistributioncurves(EDCs)throughtheFermiarcatkx~kW,kW+0.
0171,kW+0.
0341,andkW+0.
0451.
Thedottedblacklinesaretstothesurroundingfeatures,toemphasizetheFermiarcpeak,markedbytheblackarrows.
WeobservesignaturesoftheupwarddispersionoftheFermiarcwithincreasingkx,consistentwithabinitiocalculationsandbasictopologicaltheory.
fAnMDCwithtwolargepeakscorrespondingtotheupperWeylcones.
ThedottedgreenlinesshowanexcellenttofthepeakstoLorentzianfunctions.
gSamespectrumasa,butwithkeyfeaturesmarkedbyaquantitativetstoEDCsandMDCs.
TheyellowarrowscorrespondtothelocationoftheEDCsineandtheMDCinf.
hCartoonoftheconesandarcobservedinthedata,showingwhatisperhapsthesimplestcongurationofWeylpointsandFermiarcsthatcanexistinanyWeylsemimetal.
i–kAbinitiocalculationofTaIrTe4showingtheWeylpoints(redarrows)andFermiarc(bluearrow).
TheexcellentagreementwithcalculationsuggeststhatwehaveobservedaWeylsemimetalinTaIrTe4ARTICLENATURECOMMUNICATIONS|DOI:10.
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2h.
WealsoindicatethelocationsoftheEBkxcutsofFig.
2andtheEBkycutsofFig.
3,tobediscussedbelow.
Ourpump-probeARPESmeasurementsallowustodirectlymeasuretheelectronicstructureaboveEFinTaIrTe4andwendexcellentmatchwithcalculation.
EvidenceforaWeylsemimetalinTaIrTe4.
Nowwedemon-stratethatTaIrTe4isaWeylsemimetalbydirectlystudyingtheunoccupiedbandstructuretopinpointWeylconesandtopolo-gicalFermiarcs.
Basedoncalculation,wexkxneartheexpectedlocationsoftheWeylpoints,kxkW=0.
21andwestudyEB–kycutsinARPES,seeFig.
3a–c,withkeyfeaturesmarkedbyguidestotheeyeinFig.
3d.
Weobservetwoconefeatures,labeled1and2,connectedbyaweak,ratheratarcfeature,labeled3.
Wendthattheconesaremostpronouncedatkx~kW,butfadeforlargerkx.
Next,wepinpointtheFermiarcasasmallpeakdirectlyontheenergydistributioncurve(EDC)passingthroughky=0,seethebluecurveinFig.
3e,wherethedottedblacklineisattothesurroundingfeatures.
WefurthertrackthearccandidateforkxmovingawayfromkWandwendthatthearcdispersesslightlyupwards,byabout~10meV,seealsoSupplementaryFig.
1.
ThisdispersionisconsistentwithatopologicalFermiarc,whichshouldconnecttheWeylpointsandsweepupwardwithincreasingkx29.
WefurtherpinpointtheupperWeylconeonamomentumdistributioncurve(MDC)ofthekx~kWcut,Fig.
3f.
WendanexcellenttoftheWeylconepeakstoLorentzians.
Usingthisanalysis,wecanquantitativelytrackthedispersionsoftheWeylconesandFermiarconthekx~kWcut,Fig.
3gandSupplementaryFig.
2.
WenotethatfortheupperWeylconewetrackthebandsbyLorentziantsontheMDC.
However,fortheFermiarcandlowerWeylcone,therelativelyatdispersionrequiresustotrackthebandsintheEDCs.
TheEDCpeakischallengingtot,inpartbecausethepopulationdistributionisstronglydependentonbindingenergyforapump-probeARPESspectrum.
Asaresult,wetracktheFermiarcandlowerWeylconethroughanaivequadratictofthebandpeaks,againseeFig.
3g.
Wendthatthepeaktrainsarenearlylinear,seealsoSupplementaryFig.
2.
Basedonourpump-probeARPESspectraandabinitiocalculations,weproposethatTaIrTe4hoststwopairsofWeylpointsofchiralcharge±1atkx=±kW,connectedbyFermiarcs.
ThisparticularstructureoftwoWeylconescon-nectedbyaFermiarcisarguablythesimplestpossible,Fig.
3h.
Wecompareourresultstocalculationingreaterdetail,Fig.
3i–k.
WecaneasilymatchtheWeylcones,theFermiarcandanupperelectron-likeband,labeled5inFig.
3d.
However,wenotethatfromcalculationweexpectbands1and4toattachtoformasingleband,whileinourdatatheyappeartobedisconnected.
Wesuggestthatthisdiscrepancymayarisebecausephotoemissionfrompartofthebandissuppressedbylowcross-sectionatthephotonenergyusedinourmeasurement.
Inaddition,wedonotobservegoodagreementwiththelowerfeaturelabeled6inourcalculation,suggestingthatthisintensitymayariseasanartifactofourmeasurement.
Atthesametime,weconsistentlyobservethebroadfeaturelessintensitybelowtheFermilevelinboththeoryandexperiment.
Crucially,againwendamismatchintheFermilevel.
Inparticular,theWeylpointsareexpectedatEB~0.
1eV,butwendtheWeylpointsatEB~0.
07eV.
WenotethatthissamplewasgrowninadifferentbatchthanthesampleofFig.
2andacomparisonwithcalculationsuggeststhatthesecondsampleiselectrondopedby~30meV,incontrasttoa~50meVholedopingintherstsample.
Weproposethatthedifferenceindopingofthetwosamplesmayarisebecausetheyweregrownunderslightlyvaryingconditions.
Lastly,wenotethatthekypositionoftheWeylpointsshowsexcellentagreementintheoryandexperiment.
Insummary,weobserveanarcwhich(1)ter-minatesatthelocationsoftwoWeylpoints;(2)appearswhereexpectedinmomentumspace,basedoncalculation;and(3)dispersesupwardwithkx,asexpectedfromcalculation.
Thecones(1)aregaplessataspecickx~kW;(2)fadeforlargerkx;(3)appearwhereexpected,basedoncalculation;(4)areconnectedbythearc;(5)showupinpairsonlyonkx~kW,sothatthereareky(–1)kx(–1)kx(–1)ky(–1)kx(–1)ky(–1)kz(–1)kz(–1)kz(–1)TaAsMoxW1-xTe2TaIrTe4abc0.
20.
0–0.
20.
20.
20.
00.
0–0.
2–0.
2–0.
5–0.
5–0.
20.
00.
20.
00.
50.
00.
5–0.
50.
00.
5–0.
50.
00.
5–0.
50.
00.
5–0.
50.
00.
5ky(–1)–0.
50.
00.
5–0.
40.
00.
4–0.
50.
00.
50.
2–0.
2–0.
50.
00.
5–1+1defky(–1)kx(–1)kx(–1)kx(–1)ky(–1)Fig.
4ComparisonofWeylpointcongurations.
Weylpoints,plottedinredandblueforoppositechiralities,foraTaAs,with24Weylpoints,bMoxW1xTe2,witheightWeylpointsandcTaIrTe4,withtheminimalnumber,onlyfourWeylpoints,makingTaIrTe4aminimalTinvariantWeylsemimetal.
Thekz=0planeismarkedincyan.
d–fTheprojectionoftheWeylpointsonthe(001)surface,withtopologicalFermiarcs.
NotethattheWeylpointsareplottednumerically,whiletheFermiarcsareroughcartoonsdrawnbasedonARPESmeasurementsandabinitioresults.
TheblackframemarkstherstBrillouinzone.
ThelengthoftheFermiarcsinTaIrTe4islongerasafractionoftheBrillouinzoneascomparedtoTaAsandMoxW1xTe2NATURECOMMUNICATIONS|DOI:10.
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ThisprovidesstrongevidencethatTaIrTe4isaminimalWeylsemimetalwithfourWeylpoints.
DiscussionWecompareTaIrTe4withotherWeylsemimetalsandconsiderourresultsinthecontextofgeneraltopologicaltheory.
WeylsemimetalsknowntodateinexperimenthostagreaternumberofWeylpointsthanTaIrTe4.
Inparticular,thewell-exploredTaAsfamilyofWeylsemimetalshosts24WeylpointsandMoxW1xTe2hostseightWeylpoints8,30.
WeplotthecongurationofWeylpointsforTaAs,MoxW1xTe2,andTaIrTe4,whereredandbluecirclesdenoteWeylpointsofoppositechirality,Fig.
4a–c.
ItisalsointerestingtonotethatthelengthoftheFermiarcinTaIrTe4ismuchlongerasafractionoftheBrillouinzonethanthatofTaAsorMoxW1xTe2,whichcanbeseenclearlyintheprojectionsoftheWeylpointsonthe(001)surfaceofallthreesystems,Fig.
4d–f.
WeseethatourdiscoveryofaWeylsemimetalinTaIrTe4providestherstexampleofaminimalIbreaking,TinvariantWeylsemimetal.
OneimmediateapplicationofourresultsisthatTaIrTe4inpump-probeARPESmayprovideaplatformtoobservethetimedynamicsofcarrierrelaxationinaWeylsemimetal.
Morebroadly,ourresultssuggestthatTaIrTe4holdspromiseasasimplermaterialplatformforstudyingpropertiesofWeylsemimetalsintransportandapplyingthemindevices.
MethodsPump-probeangle-resolvedphotoemissionspectroscopy.
Pump-probeARPESmeasurementswerecarriedoutusingahemisphericalelectronanalyzerandamode-lockedTi:Sapphirelasersystemthatdelivers1.
48eVpumpand5.
92eVprobepulsesatarepetitionrateof250kHz28.
Thesystemisstate-of-thestart,withademonstratedenergyresolutionof10.
5meV,thehighestamonganyexistingfemtosecondpump-probesetuptodate31.
Thetimeandenergyresolutionusedinthepresentmea-surementswere300fsand15meV,respectively.
Thespotdiametersofthepumpandprobelasersatthesamplewere250and85μm,respectively.
Thedelaytimebetweenthepumpandprobepulseswas~106fs.
Measurementswerecarriedoutatpressures<5*1011Torrandtemperatures~8K.
Singlecrystalgrowthandcharacterization.
ForgrowthofTaIrTe4singlecrys-tals,alltheusedelementswerestoredinanargon-lledgloveboxwithmoistureandoxygenlevelslessthan0.
1ppmandallmanipulationswerecarriedoutintheglovebox.
TaIrTe4singlecrystalsweresynthesizedbysolidstatereactionwiththehelpofTeux.
Tapowder(99.
99%),Irpowder(99.
999%),andaTelump(99.
999%)withanatomicratioofTa/Ir/Te=1:1:12,purchasedfromSigma-Aldrich(Singapore),wereloadedinaquartztubeandthename-sealedunderavacuumof106Torr.
Thequartztubewasplacedinatubefurnace,slowlyheatedupto1000°Candheldfor100h,thenallowedtocoolto600°Catarateof0.
8°Ch1,andnallyallowedtocooldowntoroomtemperature.
Theshiny,needle-shapedTaIrTe4singlecrystals,seeSupplementaryFig.
3a,wereobtainedfromtheproductanddisplayedalayeredstructure,conrmedbytheopticalmicrograph,SupplementaryFig.
3b,andscanningelectronmicroscopeimages,SupplementaryFig.
3c.
TheEDXspectrumdisplaysanatomicratioTa:Ir:Teof1.
00:1.
13(3):3.
89(6),consistentwiththecompositionofTaIrTe4,SupplementaryFig.
3d.
Abinitiobandstructurecalculations.
Wecomputedelectronicstructuresusingtheprojectoraugmentedwavemethod32,33asimplementedintheVASP34–36packagewithinthegeneralizedgradientapproximation37schemes.
Experimentallatticeconstantswereused38.
A15*7*7Monkhorst-Packk-pointmeshwasusedinthecomputationswithacutoffenergyof400eV.
Thespin-orbitcouplingeffectswereincludedself-consistently.
Tocalculatethebulkandsurfaceelectronicstructures,weconstructedarst-principlestight-bindingmodelHamilton,wherethetight-bindingmodelmatrixelementsarecalculatedbyprojectingontotheWannierorbitals39–41,whichusetheVASP2WANNIER90interface42.
WeusedTad,Ird,andTeporbitalstoconstructWannierfunctions,withoutperformingtheprocedureformaximizinglocalization.
Dataavailability.
Alldataisavailablefromtheauthorsonrequest.
Received:25January2017Accepted:4August2017References1.
Weyl,H.
ElektronundGravitation.
Z.
Phys56,330–352(1929).
2.
Peskin,M.
&Schroeder,D.
AnIntroductiontoQuantumFieldTheory(PerseusBooks,1995)3.
Abrikosov,A.
A.
&Beneslavskii,S.
D.
Somepropertiesofgaplesssemiconductorsofthesecondkind.
J.
LowTemp.
Phys.
5,141–154(1971).
4.
Nielsen,H.
B.
&Ninomiya,M.
TheAdler-Bell-JackiwanomalyandWeylfermionsinacrystal.
Phys.
Lett.
B.
130,389–396(1983).
5.
Volovik,G.
E.
TheUniverseinaHeliumDroplet(ClarendonPress,2003).
6.
Murakami,S.
PhasetransitionbetweenthequantumspinHallandinsulatorphasesin3D:Emergenceofatopologicalgaplessphase.
NewJ.
Phys.
9,356(2007).
7.
Wan,X.
,Turner,A.
M.
,Vishwanath,A.
&Savrasov,S.
Y.
TopologicalsemimetalandFermi-arcsurfacestatesintheelectronicstructureofpyrochloreiridates.
Phys.
Rev.
B83,205101(2011).
8.
Hasan,M.
Z.
,Xu,S.
-Y.
,Belopolski,I.
&Huang,S.
-M.
DiscoveryofWeylfermionsemimetalsandtopologicalfermiarcstates.
Ann.
Rev.
Cond.
Matt.
Phys8,289–309(2017).
9.
Hosur,P.
&Qi,X.
RecentdevelopmentsintransportphenomenainWeylsemimetals.
Comp.
Rend.
Phys.
14,857–870(2013).
10.
Xu,S.
-Y.
etal.
DiscoveryofaWeylFermionsemimetalandtopologicalFermiarcs.
Science349,613–617(2015).
11.
Lv,B.
Q.
etal.
ExperimentaldiscoveryofWeylsemimetalTaAs.
Phys.
Rev.
X5,031013(2015).
12.
Huang,S.
-M.
etal.
AWeylFermionsemimetalwithsurfaceFermiarcsinthetransitionmetalmonopnictideTaAsclass.
Nat.
Commun.
6,7373(2015).
13.
Weng,H.
etal.
Weylsemimetalphaseinnoncentrosymmetrictransition-metalmonophosphides.
Phys.
Rev.
X5,011029(2015).
14.
Xu,S.
-Y.
etal.
DiscoveryofaWeylfermionstatewithFermiarcsinniobiumarsenide.
Nat.
Phys.
11,748–754(2015).
15.
Xu,S.
-Y.
etal.
ExperimentaldiscoveryofatopologicalWeylsemimetalstateinTaP.
Sci.
Adv.
1,10(2015).
16.
Zheng,H.
etal.
Atomic-scalevisualizationofquantuminterferenceonaWeylsemimetalsurfacebyscanningtunnelingmicroscopy.
ACSNano10,1378(2016).
17.
Yang,L.
X.
etal.
Weylsemimetalphaseinthenon-centrosymmetriccompoundTaAs.
Nat.
Phys.
11,728–732(2015).
18.
Soluyanov,A.
etal.
TypeIIWeylsemimetals.
Nature527,495–498(2015).
19.
Chang,T.
-R.
etal.
Predictionofanarc-tunableWeylFermionmetallicstateinMoxW1xTe2.
Nat.
Commun.
7,10639(2016).
20.
Sun,Y.
etal.
PredictionofWeylsemimetalinorthorhombicMoTe2.
Phys.
Rev.
B92,161107(2015).
21.
Wang,Z.
J.
etal.
MoTe2:atype-IIWeyltopologicalmetal.
Phys.
Rev.
Lett.
117,056805(2016).
22.
Belopolski,I.
etal.
FermiarcelectronicstructureandChernnumbersinthetype-IIWeylsemimetalcandidateMoxW1xTe2.
Phys.
Rev.
B94,085127(2016).
23.
Huang,L.
etal.
SpectroscopicevidencefortypeIIWeylsemimetallicstateinMoTe2.
Nat.
Mat15,1155–1160(2016).
24.
Deng,K.
etal.
ExperimentalobservationoftopologicalFermiarcsintype-IIWeylsemimetalMoTe2.
Nat.
Phys12,1105–1110(2016).
25.
Tamai,A.
etal.
Fermiarcsandtheirtopologicalcharacterinthecandidatetype-IIWeylsemimetalMoTe2.
Phys.
Rev.
X6,031021(2016).
26.
Huang,S.
-M.
etal.
NewtypeofWeylsemimetalwithquadraticdoubleWeylfermions.
PNAS113,1180–1185(2015).
27.
Koepernik,K.
etal.
TaIrTe4aternarytype-IIWeylsemimetal.
Phys.
Rev.
B93,201101(2016).
28.
Ishida,Y.
etal.
Time-resolvedphotoemissionapparatusachievingsub-20-meVenergyresolutionandhighstability.
Rev.
Sci.
Instr.
85,123904(2014).
29.
Belopolski,I.
etal.
CriteriafordirectlydetectingtopologicalfermiarcsinWeylsemimetals.
Phys.
Rev.
Lett.
116,066802(2016).
30.
Hasan,M.
Z.
,Xu,S.
-Y.
&Bian,G.
Topologicalinsulators,topologicalsuperconductorsandWeylfermionsemimetals:discoveries,perspectivesandoutlooks.
Phys.
Scrip.
T164,014001(2015).
31.
Ishida,Y.
etal.
Quasi-particlesultrafastlyreleasingkinkbosonstoformFermiarcsinacupratesuperconductor.
Sci.
Rep.
6,18747(2016).
32.
Blchl,P.
E.
Projectoraugmented-wavemethod.
Phys.
Rev.
B50,17953–17979(1994).
33.
Kresse,G.
&Joubert,J.
Fromultrasoftpseudopotentialstotheprojectoraugmented-wavemethod.
Phys.
Rev.
B59,1758–1775(1999).
34.
Kresse,G.
&Hafner,J.
Abinitiomoleculardynamicsforopen-shelltransitionmetals.
Phys.
Rev.
B48,13115–13118(1993).
35.
Kresse,G.
&Furthmüller,J.
Efciencyofabinitiototalenergycalculationsformetalsandsemiconductorsusingaplane-wavebasisset.
Comput.
Mater.
Sci.
6,15–50(1996).
ARTICLENATURECOMMUNICATIONS|DOI:10.
1038/s41467-017-00938-16NATURECOMMUNICATIONS|(2017)8:942|DOI:10.
1038/s41467-017-00938-1|www.
nature.
com/naturecommunications36.
Kresse,G.
&Furthmüller,J.
Efcientiterativeschemesforabinitiototalenergycalculationsusingaplane-wavebasisset.
Phys.
Rev.
B54,11169–11186(1996).
37.
Perdew,J.
P.
,Burke,K.
&Ernzerhof,M.
Generalizedgradientapproximationmadesimple.
Phys.
Rev.
Lett.
77,3865–3868(1996).
38.
Mar,A.
,Jobic,S.
&Ibers,J.
A.
Metal-metalvstellurium-telluriumbondinginWTe2anditsternaryvariantsTaIrTe4andNbIrTe4.
J.
Am.
Chem.
Soc.
114,8963–8971(1992).
39.
Marzari,N.
&Vanderbilt,D.
MaximallylocalizedgeneralizedWannierfunctionsforcompositeenergybands.
Phys.
Rev.
B56,12847–12865(1997).
40.
Souza,I.
,Marzari,N.
&Vanderbilt,D.
MaximallylocalizedWannierfunctionsforentangledenergybands.
Phys.
Rev.
B65,035109(2001).
41.
Mosto,A.
A.
etal.
Wannier90:atoolforobtainingmaximally-localizedWannierfunctions.
Comp.
Phys.
Commun178,685–699(2008).
42.
Franchini,C.
etal.
MaximallylocalizedWannierfunctionsinLaMnO3withinPBE+U,hybridfunctionalsandpartiallyself-consistentGW:anefcientroutetoconstructabinitiotight-bindingparametersforegperovskites.
J.
Phys.
Cond.
Mat24,235602(2012).
AcknowledgementsI.
B.
thanksDaixiangMouandAdamKaminskiforuseoftheirconventionallaserARPESsystematAmesLaboratory&IowaStateUniversityduringthepreliminaryphaseofthisproject.
I.
B.
acknowledgesthesupportoftheUSNationalScienceFoundationGRFP.
TheworkatPrincetonissupportedbytheUSNationalScienceFoundation,DivisionofMaterialsResearch,underGrantsNo.
NSF-DMR-1507585andNo.
NSF-DMR-1006492andbytheGordonandBettyMooreFoundationthroughtheEPIQSprogramgrantGBMF4547(Hasan).
Y.
I.
issupportedbytheJapanSocietyforthePromotionofScience,KAKENHI26800165.
ThisworkisalsonanciallysupportedbytheSingaporeNationalResearchFoundation(NRF)underNRFRFAwardNo.
NRF-RF2013-08,MOETier2MOE2016-T2-1-131andMOE2016-T2-2-153(S).
T.
-R.
C.
andH.
-T.
J.
aresupportedbytheMinistryofScienceandTechnology,NationalTsingHuaUniversity,NationalChengKungUniversity,andAcademiaSinica,Taiwan.
T.
-R.
C.
andH.
-T.
J.
alsothanktheNationalCenterforHigh-PerformanceComputing,theComputerandInformationNetworkingCenterofNationalTaiwanUniversity,andtheNationalCenterforTheo-reticalSciences,Taiwanfortechnicalsupport.
H.
L.
acknowledgestheSingaporeNRFunderAwardNo.
NRF-NRFF2013-03.
AuthorcontributionsTheprojectwasconceivedbyI.
B.
andP.
Y.
,withguidancefromM.
Z.
H.
I.
B.
carriedoutthepump-probeARPESmeasurementswithhelpfromD.
S.
S.
andsupportfromY.
I.
P.
Y.
synthesizedandcharacterizedthesinglecrystalTaIrTe4samplesunderthesupervisionofZ.
L.
Y.
I.
builtthepump-probeARPESset-upinthelaboratoryofS.
S.
,withadditionalsupportfromT.
K.
T.
-R.
C.
carriedouttheabinitiocalculationswithhelpfromG.
C.
andunderthesupervisionofH.
-T.
J.
andH.
L.
I.
B.
analyzedthedataandinterpretedresultswithhelpfromD.
S.
S.
,T.
-R.
C.
,S.
S.
Z.
,S.
-Y.
X.
,H.
Z.
,G.
C.
,andG.
B.
Allauthorscon-tributedtowritingthemanuscript.
AdditionalinformationSupplementaryInformationaccompaniesthispaperat10.
1038/s41467-017-00938-1.
Competinginterests:Theauthorsdeclarenocompetingnancialinterests.
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