phenalenyl基分子器件热电性质及其调控.pdf 9页

'中国科技论文在线http://www.paper.edu.cnExcellentthermoelectricpropertiesinducedbydifferentcontactgeometriesinphenalenyl-basedsingle-molecule#5devices1121Xuan-HaoCao,Wu-XingZhou,Chang-YongChen,Li-MingTang,Ke-Qiu1**Chen(1.DepartmentofAppliedPhysics,SchoolofPhysicsandElectronics,HunanUniversity,Changsha410082,China.;102.PhysicsInstitute,ShaoguanUniversity,Shaoguan512005,China)Abstract:Weinvestigatedthethermoelectricpropertiesofphenalenyl-basedmoleculardevicesbyusingthenon-equilibriumGreen’sfunctionmethodcombinedwithdensityfunctiontheory.Theresultsshowthatthethermoelectricperformanceofmoleculardevicecanbesignificantlyimprovedbydifferentcontactgeometries.TheZTvalueofM1canreach1.2atroomtemperature,whichistwo15ordersofmagnitudehigherthanthatofgraphene.Moreover,thechangeofthecouplingbetweenmoleculeandelectrodescanalsoenhancetheZTvalue.TheZTvalueofM1canbefurtheroptimizedto1.4at300Kand5.9at100Kowingtothedecreaseofelectronicthermalconductanceandalmostunchangedpowerfactor.Keywords:Condensedmatterphysics;Thermoelectricproperties;Phenalenyl-basedmolecular20devices0IntroductionThermoelectricmaterialshavetheadvantageofrealizethemutualtransformationofheatand[1]electricitywithoutmovingpartsorworkingfluids.Althoughtheyarereliable,clean,25environment-friendlyandcompactwhencomparedwithtraditionalthermalengine,itscommercial[1,2]applicationsisstilllimitedduetothelowthermoelectricconversionefficiency.Theperformanceofthethermoelectricmaterialscanbecharacterizedbyaunitlessparameter,whichis2ScalledfigureofmeritZTT.Tobecompetitivewiththeconventionalheatmachines,eph[3]theZTvalueofathermoelectricmaterialshouldbelargerthan3.However,tooptimizetheZT30valueisadifficulttask,astheelectricalconductivity,theSeebeckcoefficientS,thephononthermalconductivity,theelectronthermalconductivityandthetemperatureTarephe[4]fullycoupledwitheachother.Forinstance,andare,inmanycases,obeythee[5][6]Wiedemann-Franzlaw.TwostrategieshavebeenchosentoimprovetheZTvalue.One[7,8]approachistosearchforelectron-crystal−phonon-glassmaterials,whoseelectricalconductivity35similartocrystalwhilephononthermalconductivitylikeglassnamely,forinstanceCore-shell[9,10][11,12]Nanowiresandsuperlattices.AnothermethodistoenhancetheSeebeckcoefficientby[13]theincreaseoftheelectricaldensityofstatesattheFermilevelinlow-dimensionalstructures,[14][15,16,17][18][19,20][21,suchasquantumrings,quantumwires,antidotarrays,nanoribbons,nanotubes22][23,24]andsingle-moleculedevices.Grapheneisawondermaterialwithacombinationofmany40remarkableelectricalandthermalproperties.What’smore,ithastheadvantagesofelasticity,cheap,lowweight,materialabundance,andlarge-areadepositioncomparedwithinorganicFoundations:NationalNaturalScienceFoundationofChina(Nos.11274105and11674092)；DoctoralProgramofHigherEducationofChina(No.20130161130004)Briefauthorintroduction:CaoXuan-Hao(1991-),male,doctor,majorresearchdirection:lowdimensionalphysicsCorrespondanceauthor:ChenKe-Qiu（1964-），male，professor，majorresearchdirection:lowdimensionalphysics.E-mail:keqiuchen@hnu.edu.cn-1- 中国科技论文在线http://www.paper.edu.cnthermoelectricmaterials.However,itisnotinitiallyexpectedtobeagoodcandidateforthermoelectricapplicationforitsheatconductivityashighas5kWmK/,whichleadstoitsZT[25,26]valuediscoveredtobeonly0.01.ButrecentcomputationalworksshowthathighZTvalues45couldbereachedinmodifiedgraphenenanoribbons(GNRs)whichhaveexploitedwithquantum[27,28,29,30,31,32,33]coherenceeffects.Accordingly,modifiedgraphenenanoribbonhasrecentlyreceivedattentionasapotentialthermoelectricmaterial.ByusingmodifiedGNRsasbackbone,wecanthendesignthedevicewithhigherthermoelectricperformances.[24]Recently,Mariusetal.systematicallystudiedthethermoelectricperformanceof50paracyclophane-basedsingle-moleculejunctionswithgoldelectrodesbyusingafullyfirst-principles-basedmethod,andfindsthatitispossibletochemicallyadjustthetransportpropertiesandenhancetheZTvalue.Althoughinlaboratory-basedconductancemeasurementsgoldiswidelyemployedastheelectrodematerial.However,goldnanoelectrodesareunstableat[34]roomtemperature.Therefore,electrodeswithnanometergaphavebeenproposedusingthe[35]55sp2-bondedtwo-dimensionalcarbon-basedmaterial,GNRs.InadditiontotheexcellentstabilityandconductivityofGNRsevenathightemperaturescomparedtogold,thenotableadvantageofGNRselectrodesisthattheirFermienergyareclosematchtothemolecularorbitalsoforganic[36]moleculeswhenformsingle-moleculejunctions.Furthermore,Fanetal.theoreticallyexploredtheelectronicpropertiesofphenalenylmoleculardevicewithdifferentcontactgeometries,andthe60systematicresearchofthermoelectricpropertiesofthesephenalenylmoleculardeviceshasnotbeenreportedyet.Inthepresentwork,weinvestigatethethermoelectricpropertiesofphenalenyl-basedmoleculardeviceswithtwokindsofzigzagGNRselectrodesusingthenon-equilibriumGreen’sfunctionmethodcombinedwiththedensityfunctionaltheory.ThecomputationalresultsshowthatM11havethehighestZTvalueinM11-M31whichismainly65determinedbytheelectricaltransportpropertiesofphenalenyl-basedmoleculardevices,andtheirthermoelectricperformancecanbeoptimizedbythecouplingbetweenthephenalenymoleculeandzigzagGNRsleads.Fig.1ConfigurationsofM11(2)-M31(2).Thedashedboxrepresentsthereplacementareaofcentralmoleculeandthe70number1(2)meantwodifferentleads.-2- 中国科技论文在线http://www.paper.edu.cn1ResultsandDiscussionThemoleculardeviceswesimulatedareillustratedinFig.1.Wedividedthewholesystemintothreeparts:leftlead(hotbath),centralregionandrightlead(coldbath).Forcentralphenalenylmolecule,whichisawell-knownstableorganicradicalwithhighsymmetry,webond75ittotwozigzagGNRsusingpenta-graphene.Accordingtothedifferentcontactgeometriesbetweenthemoleculeandelectrodes,thedevicescanbedividedintoM1,M2andM3.Thesubscriptrepresentstwotypesofpenta-graphenestructures,forexampleM12indicatesthatthecentralmoleculeofdeviceisM1andtheleftandrightleadsarebothtype-2electrodesasshowninFig.1.TheinitialdistancebetweentwoGNRshasbeenoptimized.Eachelectrodehasbeen80describedasasupercellwhichcontainstworepeatedunitcellsalongthetransportdirection.Boththeedgeoftheleadsandthescatteringregionarehydrogenated.Fig.2Thermalpropertiesofalldevices.(a)Thetemperature-dependentphononthermalconductance,and(b)ThephonontransmissionspectrumsofM11-M31and4ZGNR.85Thecalculatedphononthermalconductanceandphonontransmissionfunctionsfor4ZGNRandM11(2)-M31(2)wereillustratedinFigs.2(a)andFigs.2(b).Inbothfiguresofphononthermalconductanceandphonontransmissionspectrum,wecanclearlyseethatthephononthermalconductanceof4ZGNRwillbelargelyreducedbyintroducingthemolecule.Whatismore,inallthetemperatureweconsidered,althoughthedifferenceincreaseswiththeraiseoftemperature,the90valueofphononthermalconductanceofthesesixmoleculardevicesisnotchangetoomuch.Nevertheless,fromFig.2(b),wecanfindthatthediscrepancyofthephonontransmissionfunctionofthreemodelsisalsonotobviouslyobserved.Asthetemperaturerises,graduallyexcitedhighfrequencyphononmodeswillnotsignificantlyexpandthesedifferences.Therefore,thisexplainsthecauseoftinydifferenceofphononthermalconductancebetweenthesesixstructures,95indicatingthephononthermalconductancewillnotsignificantlyinfluencethethermoelectricperformanceofourmoleculardevices.Torevealwhetherthedifferentcontactgeometriestozigzag-edgegrapheneleadscanaffectthethermoelectricpropertiesofphenalenyl-basedmolecularjunctions,wecomputedtheelectricalpropertiesofM11-M31and4ZGNR.Fig.3(a)-3(c)showtheSeebeckcoefficientS,powerfactor2100S,electricalconductanceandelectricalthermalconductioneofthesefourconfigurationsatroomtemperature,respectively.Ingeneral,wecanidentifythatelectricalpropertiesofthedevicescanbemarkedlymodifiedbychangingthetypeoftheconnectiongeometrybetweenelectrodesandmolecule.Furthermore,comparedtoM21andM31,M11haveadmirablepowerfactorwhichcanrivalto4ZGNR(seeFig.3(c)).Fortunately,unlikethe105extremelyhighelectronconductanceof4ZGNR,theelectricalthermalconductanceofM11has-3- 中国科技论文在线http://www.paper.edu.cnbeensignificantlyreducedasshowninFig.3(b).Inadditiontothephononpropertiesstudiedabove,reduceofelectronthermalconductancecannotablyenhancethethermoelectricefficiencyofM11comparedwith4ZGNR.ThesituationofM21andM31aredifferentfromM11,wecanfindthattheelectricalconductanceisfallenmuchfromFig.3(a)-3(c),whiletheSeebeckcoefficient110havealmostthesamevalueofM11atthepointofchemicalpotentialwherepowerfactorobtainthemaximumvalue,leadingtheaggravationofpowerfactorofM21andM31.Therefore,theelectricalconductanceofM11-M31isthemainfactorwhichleadstothelargedifferencesinthepowerfactorofthesethreemolecularmodels.115Fig.3ThermoelectricpropertiesofM11-M31and4ZGNR.(a)Seebeckcoefficient,(b)electricalconductanceandelectronthermalconductance,(c)powerfactor,(d)FigureofmeritZTofallmodelsasafunctionofchemicalpotentialatroomtemperature.Totracetheoriginofthisphenomenon,weobtainthemolecularprojectedself-consistentHamiltonian(MPSH)energyspectrumofthetwofrontiermolecularorbitals,whicharecalled120HOMO(highestoccupiedmolecularorbital)andLUMO(lowestunoccupiedmolecularorbital),ofthesethreemolecularconfigurations(Fig.4).Inmolecularelectronics,weknowthattheelectrontransportismainlydependsonfrontiermolecularorbitalsinmoleculardevice.BecausetheHOMOandLUMOarearrangedonthesidesofthenearestlocationofFermilevel,theycanexertmostdirectinfluenceontheelectronictransportofmoleculardevices.Furthermore,spatial125distributionsoforbitals,themolecularprojectedself-consistentHamiltoniannamely,canrevealtheelectronictransportofmoleculardevices.Inotherwords,iforbitalsevenlydistributeonthespaceortheextensibilityoforbitalsthroughouttheentiremolecule,thecontinuityoforbitalmayfacilitatetheelectronictransmissionandviceversa.ByinvestigatetheseMPSHenergyspectrums,wecanseethattheHOMOandtheLUMOofM11arenonlocal(Fig.4(a)andFig.4(d)),M21only130haveLUMOisnonlocal(Fig.4(e))andbothofHOMOandLUMOofM31arelocal(Fig.4(c)andFig.4(f)).Therefore,theelectricperformanceofthesethreemodelsisintheorderofM11>M21>M31,whichisagreedwiththetotalelectricalconductionrelationshipdescribedinFigs.3(b).Ingeneral,accordingtoFig.4andFig.3(b),M11haveabiggerelectricalconductionthanM21andM31atthechemicalpotentialwherepowerfactorgetthemaximumvalue.Nevertheless,spatial135distributionsoforbitalsisjustonefactortoaffecttheelectronicperformanceofmoleculardevices,anotheristhepositionoftheenergyoffrontiermolecularorbitalsinmolecularwhichcanbeindirectlydisplayedbytheFig.3(b).AlthoughtheextensibilityofHOMOandLUMOofM21is-4- 中国科技论文在线http://www.paper.edu.cnbetterthanM31,butastheZTobtainmaximumvaluetheelectricalconductionofthedevicesareaffectedbytherelativepositionofthemolecularorbitalstothechemicalpotential,whichleadto140theelectricalconductionofM31isgreaterthanM21.Fig.4MPSHofthehighestoccupiedmolecularorbitalandthelowestunoccupiedmolecularorbitalforthecentralregionofM11-M31atthezerobias.Byusingthephononandelectricalpropertieswhichcalculated,wecanobtaintheZTvalue145ofthesedevices.InFig.3(d)chemicalpotentialdependenceofthethermoelectricfigureofmeritofthesefourstructuresatroomtemperatureissummarized.WenotethattheZTofthesemoleculardevicescanbegreatlyaffectedbythechangeofthecontactgeometriesandM11hasthebestthermoelectricperformanceamongM11-M31,theZTvaluecanreach1.2,followedby0.4ofM31and0.1ofM21.Nevertheless,bycomparingFig.3(c)andFig.3(d),wecannoticethatZT150almosthavethesametrendaspowerfactor,indicatingthephononpropertieswillnotsignificantlyinfluencetheZTvalueofM11-M31.Ingeneral,excellentthermoelectricperformanceofM11ismainlyinducedbytheelectricalconductancewhichlargerthanM21andM31.Furthermore,owingtothephononthermalconductanceandelectricalthermalconductancehavethesameorderofmagnitude,thecontributionofphonontothetotalthermalconductancecannotbeneglectedfor155single-moleculedevices.Inordertofurtherimprovethefigureofmerit,weinvestigatedtheinfluenceofthecouplingbetweenmoleculeandelectrodesandtemperaturetothethermoelectricpropertiesofthesedevices.Therefore,weplottheelectricalthermalconduction(Fig.5(b))andthepowerfactor(Fig.5(c))asafunctionoftemperature.ContrasttoM11,M12hasalowerelectronthermalconductancewhile160thepowerfactorisalmostunchangedatthetemperatureof300K.AccordingtotheformulaofZT,wecanderivethatZTvaluewillberaiseasthetotalthermalconductancedecreasewhenhavealmostthesamepowerfactor.Byviewingtheelectronictransportspectrumsofdevices(Fig.6),wecanknowthatthetransportspectrumwillhaveadisplacementwhenchangingthecouplingbetweenthemoleculeandtheelectrodes.TheinsetsinFig.6showthattheelectricalconductance165willhavethesametrendastransportspectrum.Therefore,thesephenomenawillleadtothedecreaseofelectricalconductanceandelectronthermalconductanceofM1typeofmoleculardevice.Consequently,theZTvaluesofM12canbeenhancedto1.4atroomtemperature(seeinFig.5(a)).Furthermore,M2andM3typeofdevicesarealsohavesimilarphenomenon,the-5- 中国科技论文在线http://www.paper.edu.cndifferenceisthatthechangeofcouplingmakethepowerfactorofM22andM32dramatically170declined,whichmakestheZTvaluealsobereduced.Fig.5Temperature-dependentthermoelectricpropertiesofM11(2)-M31(2).(a)FigureofmeritZTofdevicesasafunctionofchemicalpotentialat300K.(b)Electronthermalconductance,(c)powerfactorand(d)ZTmaxofM11(2)-M31(2)asafunctionoftemperature.175WefurtherinvestigatedthemaximumZTvalueofthesixmodelsatdifferenttemperature(Fig.5(d)).Fromthefigure,wecanobtainthatthemaximumZTvalueofallstructuresaredecreaseasthetemperatureincreaseandtheZTofM12canreachto5.9at100K.Thereasonsforthesephenomenonarethatalthoughtheriseoftemperaturecanmakeanincreaseinthevalueof2ST,itcannotset-offthenegativeeffect,whichcausingbytheremarkablegrowthofthe180,leadingthemaximumZTreduceasthetemperatureraise.Inaddition,theelectricalephthermalconductionofM12isabouttwotimessmallthanM11,makingtheZTvalueofM12almostimproveddoubletimesthanM11.Fig.6Theelectronictransmissionspectrumsofallstructures.Theinsetsarethechemical-dependentofelectrical185conductance.-6- 中国科技论文在线http://www.paper.edu.cn2MethodThegeometricaloptimizationofthemodelsandareobtainedbyusingtheViennaAbinitio[37,38]simulationpackageandthestandardofforceconvergenceoneachatomissmallerthan0.01e/VA.Moreover,thephonon-phononinteractioninGNRshasbeenignoredforthelonger[39]190phononmean-free-path.Theinteractionbetweennucleusandextra-nuclearelectronshasbeen[40]describedwiththeprojectoraugmented-wave(PAW)pseudopotentials.Thespecificcalculation[41]detailcanrefertothiswork.TheelectronHamiltoniansandtheelectrontransmissionfunction[42,43]areperformedbyusingATOMISTIXTOOLKIT.Thecoreelectronshavebeenrepresentedwithnorm-conservingpseudopotentialswhilethelocal-densityapproximation(LDA)hasbeen195usedtotheexchange-correlationpotential.Thek-pointsamplingis(1,1,100)atthex,y,zdirection,andthecutoffenergyissetto150Ry.Adouble-zetapolarized(DZP)basissetisusedforelectronwavefunctionwhiletheconvergencecriteriaoftheHamiltonianandtheelectron-5densityare10.What’smore,theelectron-phononinteractionhasbeenneglectedduetothe[44]weakelectron-phononcouplinginGNRs.200Intheframeworkofdensity-functionalperturbationtheory(DFPT)wecangettheforce[45]constantmatrices.OncetheforceconstantmatricesKareobtained,weusethenon-equilibriumGreen’sfunction(NEGF)methodtocalculatethecorrespondingparametersinthephonontransmissionfunction:raTTraceG()CLGCR(1)205ThenthephononthermalconductancecanbecalculatedbyLandauformula:1nT,phdTph2T,(2)herenT(,)istheBose-Einsteindistributionfunctionandisthefrequencyofphonons39.HavingobtainedtheelectrontransmissionfunctionTEe()byusingdensity-functionaltheory(DFT)combinedwithNEGF,wecanthenderivetheSeebeckcoefficientS,theelectronic210conductance,andtheelectronthermalconductanceeviaLorenzfunction:2nfE,,TL(,)TTEE()()dEnehE,(3)wherefE(,,)TisFermi-DiracdistributionfunctionattemperatureTandchemicalpotential.3Conclusion215Insummary,weinvestigatethethermoelectricpropertiesofphenalenyl-basedsingle-moleculedevicesusingthenon-equilibriumGreen’sfunctionmethodcombinedwiththedensityfunctionaltheory.Wefindthatthethermoelectricpropertiescanbelargelyregulatedbychangingthecontactgeometryofphenalenylmolecule,whichismainlyaffectedbythedifferentoftheelectricaltransportperformance.Moreover,thethermoelectricperformanceofthese220moleculardevicesincreaserapidlywiththedecreaseoftemperature,indicatingthesedevicesareprefertoeffectivityuseatlowtemperatureandroomtemperature.Inaddition,wefindthatthechangeofcouplingbetweenmoleculeandelectrodescanalsoenhancetheZTvaluesignificantly.TheresultsshowthatM11andM12havegreatpotentialtothermoelectricapplicationinthefuture.-7- 中国科技论文在线http://www.paper.edu.cnAcknowledgements225ThisworkwassupportedbytheNationalNaturalScienceFoundationofChina(Nos.11274105and11674092),bytheSpecializedResearchFundfortheDoctoralProgramofHigherEducationofChina(No.20130161130004),andbyopenResearchFundProgramoftheStateKeyLaboratoryofLow-DimensionalQuantumPhysics.TheauthorsthanktheNationalSupercomputerCenterinChangshaforthecomputingresourcesprovided.230References[1]KimGH,ShaoL,ZhangK,etal.Engineereddopingoforganicsemiconductorsforenhancedthermoelectricefficiency[J].NatureMaterials,2013,12(8):719-723.[2]ZebarjadiM,EsfarjaniK,DresselhausMS,etal.Perspectivesonthermoelectrics:fromfundamentalstodeviceapplications[J].Energy&EnvironmentalScience,2012,5(1):5147-5162.235[3]JiangJW,WangJS,LiB.AnonequilibriumGreen"sfunctionstudyofthermoelectricpropertiesinsingle-walledcarbonnanotubes[J].JournalofAppliedPhysics,2011,109(1):014326.[4]MahanG,SalesB,SharpJ.Thermoelectricmaterials:Newapproachestoanoldproblem[J].PhysicsToday,1997,50(3):42-47.[5]JonsonM,MahanGD.Mott"sformulaforthethermopowerandtheWiedemann-Franzlaw[J].Physical240ReviewB,1980,21(10):4223.[6]ChenG,DresselhausMS,DresselhausG,etal.Recentdevelopmentsinthermoelectricmaterials[J].InternationalMaterialsReviews,2003,48(1):45-66.[7]HochbaumAI,ChenR,DelgadoRD,etal.Enhancedthermoelectricperformanceofroughsiliconnanowires[J].Nature,2008,451(7175):163-167.245[8]WangJS,WangJ,LüJT.Quantumthermaltransportinnanostructures[J].TheEuropeanPhysicalJournalB,2008,62(4):381-404.[9]ZhouWX,ChenKQ.Enhancementofthermoelectricperformancebyreducingphononthermalconductanceinmultiplecore-shellnanowires[J].Scientificreports,2014,4:7150.[10]LiuYY,ZhouWX,TangLM,etal.Core-shellnanowireservesasheatcable[J].AppliedPhysicsLetters,2502013,103(26):263118.[11]ChenXK,XieZX,ZhouWX,etal.Phononwaveinterferenceingrapheneandboronnitridesuperlattice[J].AppliedPhysicsLetters,2016,109(2):023101.[12]BalandinAA,LazarenkovaOL.Mechanismforthermoelectricfigure-of-meritenhancementinregimentedquantumdotsuperlattices[J].AppliedPhysicsLetters,2003,82(3):415-417.255[13]MurphyP,MukerjeeS,MooreJ.Optimalthermoelectricfigureofmeritofamolecularjunction[J].PhysicalReviewB,2008,78(16):161406.[14]Saiz-BretínM,MalyshevAV,OrellanaPA,etal.Enhancingthermoelectricpropertiesofgraphenequantumrings[J].PhysicalreviewB,2015,91(8):085431.[15]WangB,ZhouJ,YangR,etal.Ballisticthermoelectrictransportinstructurednanowires[J].NewJournalof260Physics,2014,16(6):065018.[16]ZhangG,ZhangQ,BuiCT,etal.Thermoelectricperformanceofsiliconnanowires[J].AppliedPhysicsLetters,2009,94(21):213108.[17]FangH,FengT,YangH,etal.Synthesisandthermoelectricpropertiesofcompositional-modulatedleadtelluride-bismuthtelluridenanowireheterostructures[J].Nanoletters,2013,13(5):2058-2063.265[18]YanY,LiangQF,ZhaoH,etal.Thermoelectricpropertiesofone-dimensionalgrapheneantidotarrays[J].PhysicsLettersA,2012,376(35):2425-2429.[19]OuyangT,XiaoH,XieY,etal.Thermoelectricpropertiesofgamma-graphynenanoribbonsandnanojunctions[J].JournalofAppliedPhysics,2013,114(7):073710.[20]ZhouB,ZhouB,ZengY,etal.Seebeckeffectsinagraphenenanoribboncoupledtotwoferromagnetic270leads[J].JournalofAppliedPhysics,2014,115(11):114305.[21]ZhouWX,TanS,ChenKQ,etal.EnhancementofthermoelectricperformanceinInAsnanotubesbytuningquantumconfinementeffect[J].JournalofAppliedPhysics,2014,115(12):124308.[22]ChenJ,ZhangG,LiB.RemarkableReductionofThermalConductivityinSiliconNanotubes[J].NanoLetters,2010,10:3978-3983.275[23]TanCM,ZhouYH,ChenCY,etal.Spinfilteringandrectifyingeffectsinthezincmethylphenalenylmoleculebetweengraphenenanoribbonleads[J].OrganicElectronics,2016,28:244-251.[24]BürkleM,HellmuthTJ,PaulyF,etal.First-principlescalculationofthethermoelectricfigureofmeritfor[2,2]paracyclophane-basedsingle-moleculejunctions[J].PhysicalReviewB,2015,91(16):165419.[25]ZuevYM,ChangW,KimP.Thermoelectricandmagnetothermoelectrictransportmeasurementsof280graphene[J].PhysicalReviewLetters,2009,102(9):096807.[26]XuY,LiZ,DuanW.Thermalandthermoelectricpropertiesofgraphene[J].Small,2014,10(11):2182-2199.[27]TanSH,TangLM,XieZX,etal.Effectofpentagon-heptagondefectonthermaltransportpropertiesingraphenenanoribbons[J].Carbon,2013,65:181-186.[28]NiX,LiangG,WangJS,etal.Disorderenhancesthermoelectricfigureofmeritinarmchairgraphane285nanoribbons[J].AppliedPhysicsLetters,2009,95(19):192114.-8- 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