石墨烯纳米带电子输运性质的声子调控机理.pdf 8页

'中国科技论文在线http://www.paper.edu.cnTheelectrontransportmodulatedwithphononingraphene#nanoribbons**5Yue-YangLiu,Bo-LinLi,Shi-ZhangChen,Ke-QiuChen(SchoolofPhysicsandElectronics,HunanUniversity,Changsha,410082)Abstract:Weobservedirectlythelatticevibrationanditsmultifoldeffectonelectron/spintransportinzigzaggraphenenanoribbonsinsimulation.Resultsshowthattheelectrontransportfluctuatesgreatlyduetotheincessantlatticevibrationofthenanoribbons.Moreinterestingly,thephononsbehavelikea10double-edgedswordthatitbooststheconductanceofsymmetriczigzagnanoribbons(containingevennumberofzigzagchainsalongthewidthdirection)whileweakenstheconductanceofasymmetricnanoribbons.Asaresult,thespinfiltereffectthatexistsinperfectsymmetriczigzaggraphenenanoribbonissignificantlyweakenedbyphonons.Sincephononsareusuallyinevitableinexperiments,theresearchisverymeaningfulforguidingtherealizationoftheoreticalphenomenainexperimentsor15explainingthemismatchesbetweentheoreticalpredictionsandexperimentalresults.Keywords:Condensedmatterphysics;Electron-phononinteraction;Latticevibration;Electrontransport;Graphenenanoribbons0Introduction20Grapheneandgraphenenanoribbons(GNRs),whichbringusthewonderandprosperityoftwo-dimensionalmaterials,havedrawntremendousattentionfromresearchersduetotheir[1-8][9-17]distinctiveelectronicandthermalpropertiesandsoon.Zigzaggraphenenanoribbons(ZGNRs)areespeciallyattractiveinnanoelectronicsandspintronicsbecausemagneticedge[18-20]stateshavebeenfoundtobeexistattheiredges,andalotofintriguingtransportproperties25havebeenpredictedinZGNRs.Forexample,Sonetal.havedemonstratedthathalf-metallicityandspin-polarizedcurrentscanbeobtainedinZGNRsbyapplyinglateralelectricfieldsand[21]splitgates;Kimetal.reportedtheextraordinarylargemagnetoresistancesinGNR-based[22]spin-valvedevices.Impressively,Lietal.findthattheelectrontransportpropertiesof[23]ZGNRsarecloselyrelatedtothesymmetryofthenanoribbonsalongthewidthdirection,30whichdividestheZGNRsintotwotypes.Later,itisfoundthatZGNRswithsymmetryalongthewidthdirectionshowsperfectspinfiltereffectwhenthespinsofthetwoendsofthe[24]nanoribbonaresettobeanti-parallel.AllthesepropertiessuggestthegreatpotentialapplicationofZGNRsonelectronicsandspintronics.However,wenoticethatwhilemostofthetheoreticalstudiesarebasedonperfecttwo-dimensionallattices,thegrapheneandgraphene35nanoribbonsfabricatedinexperimentsareactuallydecoratedwithripplesandshouldbe[3,25]vibratingduetothermalexcitedlatticewavesorphonons.ThusitisnaturaltowonderwhetherthepredictedtransportpropertiesofZGNRsbasedonperfecttwo-dimensionallatticesarestillvalidwhenphononsaretakenintoconsideration,andwhetherwecanreallyobtainthepredictedpropertiesorphenomenainexperiments.40Infact,effortshavebeenmadetoinvestigatetheelectron-phononinteractioningraphenenanoribbons.Forexample,Drothetal.havemadeacommentontheeffectofacousticphonons[26]onspinrelaxationingraphenenanoribbons;Lietal.reportedtheeffectofharmonicphonons[27]ontheelectrontransportofsymmetricZGNRs.However,wenoticethatthemethodsFoundations:NationalNaturalScienceFoundationofChina(11674092,11274105);SpecializedResearchFundfortheDoctoralProgramofHigherEducationofChina(20130161130004)Briefauthorintroduction:Yue-YangLiu(1989-),male,PhD,majorresearchdirecitons:thermaltransport,electron-phononinteraction,thermalenergyconversionCorrespondanceauthor:Ke-QiuChen(1964-),male,professor,majorresearchdirections:nanoelectronics,nanophononics,energyconversionmechanisms.E-mail:keqiuchen@hnu.edu.cn-1- 中国科技论文在线http://www.paper.edu.cnadoptedbypreviousworksarescarcelyabletoconsidertheeffectofallphononsatthesame45time,nottomentiontheinteractionofeachphonon.Thatmeansthetheoreticallyconsideredelectron-phononinteractionisdifferentfromthecaseinrealityorexperiments.Moreover,whethertheelectrontransportsindifferentkindsofZGNRsreactsimilarlytophononsornothasnotbeeninvestigated.Inthiswork,weutilizeacombinedmethodtoobservethelatticevibrationandthephonon-influencedelectrontransportinbothsymmetricZGNRsand50asymmetricZGNRs,andallphononsandtheirinteractionsareconsideredsimultaneously.ItisinterestingtofindthatphononseffectoppositelyonchangingthemagnitudeoftheconductanceofsymmetricZGNRsandasymmetricZGNRs,andtheconductanceofallnanoribbonspresentsafluctuatingfeature,whichwedeemisoneoriginoftheknownshotnoise,duetotheexistenceofphonons.Inthequeryfortheunderlyingmechanism,wefindthatthewavefunction55distributioninthescatteringregionplaysakeyroleintheelectrontransportofthenanoribbon.WealsofindthatboththespinupcurrentandspindowncurrentinsymmetricZGNRsaregreatlyenhancedbyphonons,andthusthepredictedspinfiltereffectinidealZGNRsarefoundtobegreatlyweakened.Sincephononsareusuallyinevitableinexperiments,webelieveourworkisverymeaningfulforguidingtherealizationoftheoreticalphenomenainexperimentsor60explainingthemismatchesbetweentheoreticalpredictionsandexperimentalresults.Wealsothinktheresearchisenlighteningforinvestigatingothertwo-dimensionalmaterials.1MethodsTwokindsofZGNRsareinvestigatedinthiswork.OnekindofZGNRcontains8zigzagchainsalongthewidthdirection,andthusiscalled8ZGNR.Theotherkindcontains9zigzag65chainsalongthewidthdirection,andthusiscalled9ZGNR.Latticevibrations,especiallytheirinfluenceonthesymmetryofthenanoribbonsareinvestigatedbyutilizingtheGeneralUtility[28]latticeprogram(GULP),whichisapackagebasedonlatticedynamics.Theinteratomic[29]forcesbetweenC-C,C-HandH-HarealldescribedbytheBrennerpotential.Beforecalculatingthephonondispersionrelationshipandthevibrationmodevectors,thetwokindsof70ZGNRunitcellsarebothoptimizedbytheGULPpackagetillaaccuracyof1e-7eV/Åisreached.Whentheunitcelliswelloptimized,itisexpandedintoananoribbonwith13unitcellsalongthelengthdirection.Thephononsarethenintroducedbyoptimizingthestructurewithmoleculardynamics,whichhastakentheanharmoniceffectsofphononsintoconsideration,bythe[30]75LAMMPSpackage.Indetail,thenanoribbonisfirstputintoaNVTensemble,whereTequalsto300K,for5millionsteps(2.5nanoseconds)toequilibriumthesystem,andthenthestructureofthenanoribbonisexportedevery0.1nanosecondsfor1.6nanoseconds.Whenallthestructuresare[31,32]obtained,theAtomistixToolKit(version2016.3),whichisbasedonDensityFunctionalTheory(DFT)andNon-equilibriumGreenFunction(NEGF)approach,isutilizedtocalculatethe80electrontransportineverystructure.TheDFTcalculationsareperformedunderthelocal-densityapproximation(LDA)exchange-correlationfunctionandthesingle-polarized(SZP)basisset.Itisworthtomentionthattheleft-mosttwounitcellsandtheright-mosttwounitcellsofthenanoribbonsarefixedfrozenbeforethesimulationsothattheycanserveasthescreeningregionsandelectrodesforcalculatingtheelectrontransportinthelaterpartofthiswork.852ResultsanddiscussionsFig.1showsthechangingstructureofavibratingZGNR.ThestructuresoftheZGNRat-2- 中国科技论文在线http://www.paper.edu.cntwodifferentmomentsarebothobtainedfrommoleculardynamicssimulations.Itcanbeseenthatalthoughsomeatomsmoveveryslightly,mostoftheatomsmoveawayfromtheirpreviouspositionssignificantlyastimepassesby.Suchheat-induceddeviationhasbeenreportedtobe[33,34]90abletotriggerpiezoelectricitytoproduceelectricityinpiezoelectricmaterials,andableto[35-37]formstandingwaveinasymmetricnanowirestoenhancethermalrectification.Moreimportantly,theHatomsattheleftsideofthenanoribbonmovedupwhilethatattherightsideofthenanoribbonmoveddown,indicatingthatthestructureisnolongercompletelytwo-dimensionalandthesymmetryofthenanoribbonhasbeendestroyedtosomeextent.95Fig.1Thechangingstructureofavibratingzigzaggraphenenanoribbon.TheCandHatomsattwodifferentmomentsareidentifiedbygrayandsilver,redandgreen,respectively.TocomprehensivelyunderstandthelatticevibrationofZGNRs,wecalculatethephonon100dispersionrelationshipandthevibrationmodevectorsofthe8ZGNR.AsisseeninFig.2,thereareindeedphononmodesthatcandestroythesymmetryofthenanoribbons,includingbothin-planevibrationmodeandout-planevibrationmode.Anditisworthtoemphasizethatalthoughonlytwovibrationmodes,whosefrequenciesandwavevectorsaremarkedatthedispersionrelationship,areplottedinFig.2,thereisnodoubtthatmanyothervibrationmodes105withdifferentfrequenciesandwave-lengthsexistinthenanoribbonsareabletodestroythesymmetryofthenanoribbons.Wecanthusforecastthegreateffectofphononsontheelectronandspintransportinzigzaggraphenenanoribbons.110Fig.2Thephonondispersionrelationshipandtwoofthesymmetry-breakingvibrationmodesof8ZGNR.(a)-3- 中国科技论文在线http://www.paper.edu.cnanout-of-planevibrationmode.(b)phonondispersionrelationship.(c)anin-planevibrationmode.Fig.3Theeffectofphononsandribbonwidth(symmetry)ontheconductanceofZGNRs.(a)I-tcurveofthe1158ZGNRsand9ZGNRsunderabiasof0.5V.(b)I-Vcurveofthe8ZGNRsand9ZGNRsatacertiantime.Inconsistentwithpreviousreport,itisseeninFig.3(a)thattheelectriccurrentinducedbyabiasof0.5Vintheideal8ZGNRismuchsmallerthanthatintheideal9ZGNRduetothe[23]suppressionoftheelectrontransportbythesymmetryofthe8ZGNR.However,when120phononsareintroduced,theelectriccurrentofallnanoribbonsturnsouttobefluctuatingwithtimeduetotheincessantchangeofthevibratingstructure.Moreimportantly,itisseenthattheelectriccurrentthatpassesthroughthe9ZGNRdecreasessignificantlywhilethecurrentthroughthe8ZGNRincreasesalotwhenphononsareintroduced.Thedecreaseofthecurrentin9ZGNRisaccessiblebecauseitiswellknownthatphononsscatterthetransportofelectrons.125However,theincreaseofthecurrentinphonon-influenced8ZGNRisnotexpected.Tobeprudent,wecheckthedependenceoftheelectriccurrentsontheappliedbiasvoltagetoseewhetherthephenomenonexistsonlyatcertainbiases.AsisseeninFig.3(b),thedecreaseofthecurrentin9ZGNRandtheincreaseofthecurrentin8ZGNRaresignificantandstableundereveryappliedbiasvoltage,indicatingthatthephenomenonisgeneral.130Tofigureouttheunderlyingmechanismoftheincreaseofthecurrentin8ZGNR,wecheckthetransmissionspectraoftheideal8ZGNRandthe8ZGNR-Phonon9(labeledinFig.3(a))underabiasvoltageof0.5V.Theelectronsareexpectedtosetofffromthebandoftherightelectrodetothebandoftheleftelectrodewhenabiasvoltageof0.5Visappliedtothenanoribbon,asisshowninFig.4(a)and4(b).ItisseeninFig.4(c)thattheelectrontransmission135coefficientintheideal8ZGNRisalwayszeroneartheFermienergywhileatransmissionpeakappearsinthetransmissionspectrumofthe8ZGNR-Phonon9.Thepeakissupposedtobe-4- 中国科技论文在线http://www.paper.edu.cnresponsiblefortheincreaseofthecurrentinphonon-influenced8ZGNRbecauseotherpartsofthetwotransmissionspectracoincidewitheachother.InspiredbythepreviousreportthatthesuppressionoftheelectrontransportinidealZGNRsisrelatedtothewavefunctionofthe[23]140nanoribbon,wecheckthewavefunctionofthecentralregionenergylevelthatcorrespondstothetransmissionpeakof8ZGNR-Phonon9.Fig.4Energyband,transmissionspectraandwavefunctionsofidealZGNRandphononexistedZGNR.(a)145and(b)thebandstructureoftheleftelectrodeandtherightelectrode;(c)thetransmissionspectrumoftheideal8ZGNRand8ZGNR-Phonon9.(d)and(e)thewavefunctiondistributioninideal8ZGNRand8ZGNR-Phonon9.Thereasonwhyconductanceisincreasedbyphononsisillustratedinthisfigure.AsisseeninFig.4(d),thewavefunctiondistributioninthecentralregionoftheIdeal1508ZGNRisstrictlyoddsymmetricalongthewidthdirectionofthenanoribbon,whichisinagreementwithpreviouswork.Sincethewavefunctionofthebandintherightelectrodeis[23]oddsymmetricwhilethatofthebandintheleftelectrodeisevensymmetric,wecanimaginethattheoddsymmetricelectronssetofffromtherightelectrodewillenterthecentralregionbutwon"tbeabletoentertheleftelectrodeduetothemismatchofthesymmetryofthe155wavefunction.Thetransmissioncoefficientwillthusbenearlyzero,asisseenintheblacklineofFig.4(c).Incontrast,whenphononsareintroduced,thestructureofnanoribbonsarenolongerstrictlysymmetricalongthewidthdirection.Consequently,thewavefunctionsoftheenergylevelsinthecentralregionarealsofreefromsymmetry.AsisseeninFig.4(e),thewavefunctiondistributionin8ZGNR-Phonon9istotallydifferentfromthatofideal8ZGNR,160anditturnsouttobeveryspecial.Indetail,itcanbeseenthatthewavefunctionneartherightelectrodeisoddsymmetric,whichissameasthatoftherightelectrode.However,thewavefunctionneartheleftelectrodeisevenasymmetric,whichisjustthesameasthatoftheleftelectrode.Lyinginthemiddleisasymmetry-freepart.Itmeansthattheoddsymmetricelectronsthatcomefromtherightelectrodeareabletoenterthecentralregionandthenarealso165abletoentertheleftelectrodebecausetheoddsymmetryisnotkeptwhenelectronspassthroughthecenteralregion.That"swhyatransmissionpeakappearsinthetransmissionspectrumofthe8ZGNR-Phonon9.-5- 中国科技论文在线http://www.paper.edu.cn170Fig.5TheSpinI-Vcurveofidealandphonon-influenced8ZGNR(8ZGNR-Phonon9).(a)Spindown.(b)Spinup.Thespinfiltereffectisgreatlyweakenedbyphonons.BecausespintronicsisanimportantapplicationdirectionofZGNRs,weinvestigatetheeffectofphononsonthespintransportpropertiesof8ZGNR,whichhasbeenpredictedtohold175spinfiltereffect.Fig.5showsthespincurrentsthatpassthroughtheideal8ZGNR(Blackline)andthephononinfluenced8ZGNR(Redline).Fortheideal8ZGNR(Blackline),onlythespindowncurrentisabletopassthroughthedevicewhenapositivebiasisapplied,andonlythespinupcurrentcanpasswhenanegativebiasisapplied.Suchphenomenonistheso-calledspinfiltereffect.However,itcanbeseeninFig.5thatthespinupcurrentandspindowncurrentare180allincreasedwhenphononsareintroducedjustlikethecaseinFig.3.Consequently,theperfectspinfiltereffectin8ZGNRisgreatlyweakenedbythephonons.Nevertheless,wefindthatthespindowncurrentsundernegativebiasesincreaseslowlytolessthan15uAwhilethatunderpositivebiasesboosttoabout20uAveryquickly.Similarly,thespinupcurrentsunderpositivebiasesarealwayssmallerthanthatundernegativebiases.Thesefactsmeanthatalthoughspin185filtereffectisweakened,spinrectificationeffectisstillsignificant.3ConclusionInthispaper,weinvestigatethephonon-influencedelectrontransportofbothsymmetricandasymmetricZGNRswithacombinedmethod.Themethodproposedhereisabletoconsidertheeffectofallphononsandtheirinteractionssimultaneously,andthusismorerealthanother190methods.ResultsshowthatphononswillresultinafluctuatingconductanceinallZGNRsduetotheincessantchangeofthestructure.However,theconductanceofsymmetricZGNRswillbeincreasedbyphononswhilethatofasymmetricZGNRswillbedecreasedbyphonons.Asaresult,thepredictedspinfiltereffectinsymmetricZNGRsisweakenedtosomeextentwhenphononsexist.Theseresultsareverymeaningfulforguidingtherealizationoftheoreticalphenomenain195experimentsorexplainingthemismatchesbetweentheoreticalpredictionsandexperimentalresults.-6- 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中国科技论文在线http://www.paper.edu.cn[35]LiuYY,ZhouWX,TangLM,ChenKQ.Animportantmechanismforthermalrectificationingradednanowires.ApplPhysLett2014;105:203111-1-5.265[36]LeeJ,VarshneyV,RoyAK,FergusonJB,FarmerBL.ThermalRectificationinThree-DimensionalAsymmetricNanostructure.NanoLett2012;12:3491-96.[37]LiuYY,ZhouWX,ChenKQ.Conjunctionofstandingwaveandresonanceinasymmetricnanowires:amechanismforthermalrectificationandremoteenergyaccumulation.SciRep2015;5:17525-1-8.270石墨烯纳米带电子与自旋输运性质的声子调控机理刘岳阳，李柏林，陈仕长，陈克求（物理与微电子科学学院，湖南大学，长沙，410082）275摘要：我们直观地研究了zigzag型石墨烯纳米带的晶格振动以及其对纳米带中电子输运和自旋输运的影响。结果表明石墨烯纳米带中的电子输运由于晶格振动的存在而呈现出强烈的波动特性。更有趣的是，声子就像一把双刃剑，它增强了沿宽度方向具有镜面对称性的zigzag型石墨烯纳米带的电导，却降低了沿宽度方向没有镜面对称性的zigzag型石墨烯纳米带的电导。由于声子对电导的增强作用，存在于镜面对称zigzag型石墨烯纳米带中的自选过滤280效应被大幅度的减弱了。由于实验上一般无法避免声子的存在，我们的研究对指导实验上实现理论预言以及解释实验结果与理论结果的偏差具有非常重要的意义。关键词：凝聚态物理；电声相互作用；晶格振动；电子输运；石墨烯纳米带中图分类号：O327-8-'