Electronic and Transport Properties of Carbon Nano

arXiv:cond-mat/0301310v1[cond-mat.mtrl-sci]16Jan2003ElectronicandTransportPropertiesofCarbonNanoPeapodsA.Rochefort∗,†∗´EcolePolytechniquedeMontr´eal,D´epartementdeg´eniephysique,Montr´eal,(Qu´e)CanadaH3C3A7.†CERCA,GroupeNanostructures,Montr´eal,(Qu´e)CanadaH3X2H9.(February6,2008)AbstractWetheoreticallystudiedtheelectronicandelectricalpropertiesofmetallicandsemiconductingpeapodswithencapsulatedC60(C60@CNT)asafunc-tionofthecarbonnanotube(CNT)diameter.Forexothermicpeapods(CNTdiameter11.8˚A),onlyminorchanges,ascribedtoasmallstructuraldefor-mationofthenanotubewalls,wereobserved.Theseincludeasmallelectronchargetransfer(lessthan0.10electron)fromtheCNTtotheC60moleculesandapoormixingoftheC60orbitalswiththoseoftheCNT.Decreasingthediameterofthenanotubeleadstoamodestincreaseofthechargeden-sitylocatedbetweentheC60’s.Moresignificantchangesareobtainedforendothermicpeapods(CNTdiameter11.8˚A).WeobservealargeelectronchargetransferfromC60tothetube,andadrasticchangeinelectrontrans-portcharacteristicsandelectronicstructure.Theseresultsarediscussedintermsofπ-πinteractionandC60symmetrybreaking.TypesetusingREVTEX1I.INTRODUCTIONThepossibilityofusingnewformsofcarbon-basedmaterialsforpracticalapplicationsinnanoelectronicshasstimulatedanimportantamountofexcitingworksduringthelastdecade.[1]Sincetheirdiscoveryin1991,carbonnanotubes(CNTs)havebeenusedasanactivecomponentinthefabricationoftransistor[2–4],memoryelements[5],andmorere-cently,logiccircuits.[6,7]CNT’scanalsobeusedasatemplatefornanofabricationandasreservoirsforthestorageofgas,ions,ormetals.[8]Inthisrespect,ithasbeenrecentlyshownexperimentallythatmultipleC60moleculescanpenetrateintoacarbonnanotubetoformaone-dimensionalarrayofC60nestedinside.[9]Thisnewtypeofcarbonmaterials,duetoitsoriginalstructure,isoftencalledcarbonpeapod.FillingCNTswithC60isexothermicorendothermicdependingonthesizeofthenan-otube.[10]C60@(10,10)wasfoundtobestable(exothermic)whileotherpeapodswithasmallerCNTshellsuchasthe(9,9)and(8,8)tubesareendothermic.MetallicCNTspreservemostoftheirintrinsicpropertiesupontheencapsulationofC60molecules.TheinteractionbetweenC60andthenanotubeoccursthroughaweakorbitalmixingbetweenanearfreeelectron(NFE)stateontheCNTlocatedaboveFermilevel(andmostprobablyabovevacuumlevel)andtheporbitalsoftheC60.ThisinteractionleadstoaweakelectronconfinementbetweenC60andtheCNTwall,andaslightchargetransferfromthetubetotheC60.Therefore,onlylittleperturbationisexpected.However,recentSTMresultsshowdrasticmodificationofthelocalelectronicstructureofsemiconductingnanotubepeapods.[11]Thisperturbationisessentiallypresentintheconductionband.ThemainvariationobservedisasharpincreaseinthedensityofstatesprobeddirectlyoveranencapsulatedC60molecule.ThisincreaseintheDOSwastentativelyattributedtotheelectroniccou-plingofC60withtheCNTshell,whichisestimatedapproximatelytoabout1eV.[11]Thistube-C60couplingappearsmuchstrongerthananticipatedbytheory[10]orexperimentalworkonmetallicpeapods.[12]ItisthereforeimportanttostudyfurtherthepropertiesofencapsulatedC60ontheelectricalandelectronicpropertiesofbothmetallicandsemicon-ductingnanotubesasafunctionofthenanotubediameter.Inthepresentstudy,weshowthattheelectronicaswellastheelectrontransportpropertiesofexothermicpeapodsdonotshowdrasticdifferencesfromthepropertiesofindividualspecies.TheCNT-C60inter-actionincreasesslightlyasthenanotubediameterdecreases,butbecomesveryimportantforendothermicpeapods.II.COMPUTATIONALDETAILSWeconsideredtheencapsulationofuptothreeC60moleculesinapproximately10nmlongmetallicandsemiconductorCNTmodelscontainingupto1500carbonatoms.TheC60moleculesweresystematicallyplacedinthemiddlesectionsoftheCNT.TheregionwhereC60’sareencapsulatedisrelativelysmallwithrespecttotheentireCNTlength,thusavoidingtheinfluenceoftheopenboundaryconditionsimplicittoourfinitemodel.Thecomputedstabilizationenergy(ΔES)correspondstotheenergydifferencebetweenafullyoptimizedpeapodstructureandtheisolatedspecies(perfectCNTandisolatedC60’s).Priortotheoptimization,thedanglingbondsatbothendsofthefinitenanotubemodelswere2saturatedwithhydrogen.TheactivationenergyneededtointroducetheC60’sintheCNTwasnotevaluated.StabilizationenergieswerecalculatedwiththeMM3molecularmechanicforcefield[13](thebondparameterofalkenewasmodifiedto1.42˚A)andthegeometrieswereoptimizedwithastandardconjugatedgradienttechniquedowntoarootmeansquare(RMS)deviation10−5.Wepreviouslyshowedthatthismodified-MM3forcefieldgivesatotalenergythatisingoodagreementwiththemoreaccurateTB-DFTmethod[14].TheelectronicstructurecalculationsfortheCNTandpeapodsystemswerecarriedoutwithintheextendedH¨uckel(EH)method,whichincludesanexplicittreatmentofoverlapintegralforthesandpvalenceorbitalofcarbon.[15]IthasbeenshownthatEHgivesresultssimilartothoseobtainedonextendedCNTswithmoresophisticatedmethods.[16]Theelectricaltransportpropertiesofcarbonnanotubesandpeapodswerecomputedus-ingaGreen’sfunctionapproach[17]withintheLandauer-B¨uttikerformalism.TheHamilto-nianandoverlapmatricesusedinthisformalismwerealsodeterminedusingtheEHmodel.[15]Fortransportcalculations,thetwoendsoftheCN