Commensurate–incommensurate transition in

Commensurate–incommensuratetransitioningrapheneonhexagonalboronnitride

C.R.Woods1,L.Britnell1,A.Eckmann2,R.S.Ma3,J.C.Lu3,H.M.Guo3,X.Lin3,G.L.Yu1,Y.Cao4,R.V.Gorbachev4,A.V.Kretinin1,J.Park1,5,L.A.Ponomarenko1,M.I.Katsnelson6,Yu.N.Gornostyrev7,K.Watanabe8,T.Taniguchi8,C.Casiraghi2,H-J.Gao3,A.K.Geim4andK.S.Novoselov1*

Whenacrystalissubjectedtoaperiodicpotential,undercertaincircumstancesitcanadjustitselftofollowtheperiodicityofthepotential,resultinginacommensuratestate.Ofparticularinterestaretopologicaldefectsbetweenthetwocommensuratephases,suchassolitonsanddomainwalls.Herewereportacommensurate–incommensuratetransitionforgrapheneontopofhexagonalboronnitride(hBN).Dependingontherotationanglebetweenthelatticesofthetwocrystals,graphenecaneitherstretchtoadapttoaslightlydi erenthBNperiodicity(forsmallangles,resultinginacommensuratestate)orexhibitlittleadjustment(theincommensuratestate).Inthecommensuratestate,areaswithmatchinglatticeconstantsareseparatedbydomainwallsthataccumulatethegeneratedstrain.Suchsoliton-likeobjectsarenotonlyofsigni cantfundamentalinterest,buttheirpresencecouldalsoexplainrecentexperimentswhereelectronicandopticalpropertiesofgraphene-hBNheterostructureswereobservedtobeconsiderablyaltered.

T

heclassicalsystemwhichisusedtosimulatecommensurate–incommensuratetransitionsisaone-dimensionalchainofelasticallylinkedatomsinabackgroundperiodicpotential—theFrenkel–Kontorovamodel1.Thetwo-dimensional(2D)versionofthemodel2,3canbeappliedtoreal-lifesystems,suchasthesurfacereconstructionattheinterfacebetweentwocrystals(orbetweenacrystalandasurfacemonolayer)withcloseatomiclatticeperiods4–http://doc.guandang.netmensurate–incommensuratetransitionsin2Dhavebeendiscussed5–8andobserved9previouslyinsystemssuchasadsorbedatomsonasurfaceofacrystal.Interestingly,theboundariesbetweenthecommensuratephasescanbedescribedintermsoftopologicaldefects.Intheone-dimensionalcasesuchdefectsareusuallydescribedbysolitons1,4,10,whereasin2Dthelanguageofmisfitdislocationsiscommonlyused11.Theultimatewaytoobservesuchreconstructionwouldbebymonitoringthebehaviouroftwo2Datomiccrystalswhenplacedinclosecontact.Recentadvancesintheproductionofheterostructuresbasedon2Datomiccrystals12,and,inparticular,thepreparation13andgrowth14ofgrapheneonhBN,allowustorevisitthisproblem.hBNhasbeenoriginallyusedasasubstrate13,15andalsoanencapsulationlayer16,whichallowsminimizationofthedetrimentalinfluenceofSiO2substrates,and,asaconsequence,theachievementofspectacularelectronicqualityoftheresultinggraphenedevices.Still,thevanderWaalsinteractionbetweenhBNandgraphene,howeverweak,isnotnegligible(≈10meVpercarbonatom)17.Themismatchδ=ahBN/aG 1≈1.8%betweenthelatticeconstantsofhBN(ahBN)andgraphene(aG)andtherelativerotationangle betweenthegrapheneandhBNcrystalsleadtoahexagonalmoirépattern(Fig.1),whichhasbeenobservedbyscanningprobemicroscopy18,19.Themoirépotentialactsonchargecarriersingraphene,resultinginamodificationofitselectronicspectrum20–23.SofarithasbeenassumedthatnostructuralchangesoccuringrapheneafteritisbroughtincontactwithhBN.

Inthispaperweinvestigate(byatomicforcemicroscopy(AFM),scanningtunnellingmicroscopy(STM)andRamanspectroscopy)thestraindistributioningrapheneonhBNfordi erentmisorientationanglesbetweenthetwocrystallinestructures(whichresultsinthevariationoftheperiodLofthemoirépattern).Weobserveacommensurate–incommensuratetransitionthatoccurswhen isoftheorderofδ(thatis,≈1 ).For <δ(largeL>10nm),graphenestretcheslocallytoachieveanenergeticallyfavourablestateforvanderWaalsinteractionswithhBN,whichresultsinrelativelylargeareasofcommensuratestackinganddeformationsconcentratedinnarrowstrainedregions(similartosolitonlatticeformationinonedimension1,10).For >δ(smallmoiréperiodicity),grapheneandhBNlatticesremainunsynchronizedandtherearenodistinctregionswithaccumulatedstrain.

Oursamplesarefabricatedbythedrytransfermethod,describedindetailinrefs16,24.Inbrief,grapheneispreparedbymicromechanicalcleavage25ontopofapolymerfilmconsistingoftwosacrificiallayers.Bydissolvingoneofthem,graphenesupportedbythesecondlayercanbetransferredontopofarelativelythick(>10nm)crystalofhBN.Thenthesecondsacrificiallayerisalsoremovedandtheassemblyisannealedinaforminggasatatemperatureof～250 Ctoachieveanatomicallycleaninterface26.

ofPhysicsandAstronomy,UniversityofManchester,ManchesterM139PL,UK,2SchoolofChemistryandPhotonScienceInstitute,Universityof

Manchester,OxfordRoad,Manchester,M139PL,UK,3InstituteofPhysicsandUniversityofChineseAcademyofSciences,ChineseAcademyofSciences,Beijing100190,China,4CentreforMesoscienceandNanotechnology,UniversityofManchester,ManchesterM139PL,UK,5CenterforNano-metrology,KoreaResearchInstituteofStandardsandScience,267GajeongRo,Yuseong-Gu,Daejeon,305-340,RepublicofKorea,6InstituteforMoleculesandMaterials,RadboudUniversityofNijmegen,Nijmegen6525AJ,TheNetherlands,7InstituteofQuantumMaterialsScience,Ekaterinburg620075,Russia,8NationalInstituteforMaterialsScience,1-1Namiki,Tsukuba305-0044,Japan.*e-mail:kostya@manchester.ac.uk

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NATUREPHYSICSDOI:10.1038/NPHYS2954

thealignmentbecomeslessperfectand,atL～10nm,thepatternsuddenlybecomespracticallysinusoidal(theratiois～0.5).

Suchachangeinbehaviourcanbeexplainedbythecommensurate–incommensuratetransitionasafunctionof .Thebasicphysicsbehindsuchtransitionsisasfollows4,8,10:iftherelativerotationanglebetweenthetwocrystalsissmall(largeperiodofthemoirépattern),itbecomesenergeticallyfavourabletoadjustthetwolatticestobecomecommensurate,losinginelasticenergybutgaininginvanderWaalsenergy.Thelatterdecreasesifpreferredatomicpositionsareachievedoverthewholearea.When increasespastsomecriticalvalue(sothattheperiodofthemoirépatternbecomessmall),thegaininthevanderWaalsenergycannolongercompensatefortheelastice …… 此处隐藏：26159字，全部文档内容请下载后查看。喜欢就下载吧 ……