spin-dependent thermoelectric effects in graphene-based superconductor junctions 2017 razieh beiranvand参考.pdf

该【spin-dependent thermoelectric effects in graphene-based superconductor junctions 2017 razieh beiranvand参考 】是由【小舍儿】上传分享，文档一共【11】页，该文档可以免费在线阅读，需要了解更多关于【spin-dependent thermoelectric effects in graphene-based superconductor junctions 2017 razieh beiranvand参考 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。:..Spin-dependentthermoelectriceffectsingraphene-basedsuperconductorjunctionsRaziehBeiranvandandHosseinHamzehpourCitation:,063903(2017);doi::http://dx./:http://aip./toc/jap/121/6PublishedbytheAmericanInstituteofPhysics:..JOURNALOFAPPLIEDPHYSICS121,063903(2017)Spin-dependentthermoelectriceffectsingraphene-basedsuperconductorjunctionsRaziehBeiranvand1andHosseinHamzehpour1,2,a)1DepartmentofPhysics,,Tehran15875-4416,Iran2SchoolofPhysics,InstituteforResearchinFundamentalSciences(IPM),Tehran19395-5531,Iran(Received23November2016;accepted24January2017;publishedonline13February2017)UsingtheBogoliubov-deGennesformalism,weinvestigatethechargeandspin-dependentthermo-electriceffectsingraphene--superconductorjunctions,thereisatemperature-dependentspinthermopowerinboththegraphene-ic-ic-Rashbaspin-orbitregion--orbitinteraction,thechargeandspin-dependentSeebeckcoef?==e,,thesecoef?cientshaveazero-pointcriticalvaluewithrespecttotheicexchange?-basedsuperconductorscanbeusedinspin-.[http://dx./],42Recently,develop-1mentsinlow-temperaturemeasurementdeviceshavepro-Afterthediscoveryofgraphene,asinglelayerofvidedsuitableconditionsforexperimentalobservationinthecarbonatoms,theconceptofDiracfermionsbecamemore2–4?,-grapheneinalow-.,demonstratingthatthesignoftheSeebeckcoef?--,weneedelectron-holeasymmetryatgeometricalstructure,awidevarietyofapplicationsinelec-2,56–89–12theFermileveltoreachhigheref?ciencyinthermoelectrictronics,opto-electronics,-baseddevices,(DOSs).Halleffect,13–16chiraltunneling,17,18Kleinparadox,17,19andApplyingaspin-splitting?,-splittingsystems,thespin-–,binationofspin-orbitinteractionsinducedbyincreasingtheelectron–phononcouplingthrough(SOIs)andauniformZeeman?eldcreatesausefulmecha-,nismtomanipulatethequasi-particletransport,whichleadstoveryinterestingphenomenainthe?–51thepresenceofasuperconductingstateinmetal-:openupanewopportunityfordesigningdevicesthataretheRashbaspin-orbitinteraction(RSOI),,andtheDresselhausspin-orbitgraphene-basedjunctionsareassumedtobemesoscopicsys-interaction(DSOI),-tems,-sheetcansupportastrongRSOIofabout17meVbyproximity52whilethestrengthoftheDSOIisthisformalismleadstotheBlonder-Thinkham-Klapwijk(BTK)approach27fordescribingquantumtransportsoftheverysmall,–55Todemonstratetheexistenceofproximity-?cientandinducedRSOIinthegraphenelayer,aDCvoltagealongthethermalcurrentofgraphene-basedjunctionshavebeengraphenelayerismeasuredbyspintochargecurrentconver-–40Becauseofsion,whichisinterpretedastheinverseRashba-Edelsteinsomeexperimentallimitationsinnano-,thechargeandspin-dependentSeebeckeffectsarethespin-transportingraphene-,spin-caloritronics,whichisacombinationofthermoelectricandspintroniceffects,a)Electronicmail:******@-8979/2017/121(6)/063903/10/$,063903-1PublishedbyAIPPublishing.:..063903-,063903(2017)–36,56,57Inanon-icmateriallikegra-icfeatures(r?6or"#andr?r).Inthephene,generatingthespin-dependentSeebeckeffectthatstandardBTKapproach,thechargeandthermalconductan--equations:27,65dependentSeebeckeffecthasbeenpreviouslyreportedep=2Xformetallic,semiconductor,andeveninsulatormateri-G?gcosada1ejrr0j2jrr0j2T;41,58–-p=2r0?6umulationofmajorityandminorityspins,ep=2(2)X22andmayswitchthesignofthespin-dependentSeebeckKr?g0cosada1ejrr0jtjrr0jT;NAcoef?=2r0?6resultsrevealedalargenumberofpossibleapplicationsindesigningthermo-spintronicdevicesandincreasingtheirwherethespin-dependentnormalandAndreevre?ections61–64(rr;rr)areobtainedbymatchingthewavefunctionsattheef?-NA482tronicpropertieswithstrongenergy-dependenceofthecon-boundariesandg0?2e=hrepresentsthespin-dependentductivity,alongwithveryweakspinrelaxation,onductanceofthejunctionasafunctionofpar-promisingcandidateinspin-parisonticle’senergy,-Diracdistribu-,WdenotesthewidthofthejunctionandNreeTHerein,weconsidertwodifferentsetupsofgraphene-isthespin-dependentdensityofstate(DOS).basedjunctionsthathavepotentialfordevelopingsupercon-InasystemundertemperaturedifferencedT,theductingdeviceswithinterestingthermoelectricabilitiesunderSeebeckcoef?cientisde?nedbyvariousconditionsoftemperature,icexchange?eld,Vchemicalpotential,andspin-?;(3)dTIch?0ic-superconductor(F-S)ic-Rashbaspin-orbitwhereVisthevoltagederivedatzerochargecurrentinregion-superconductor(F-RSO-S)junctionsmadeofgra-,thebiasvoltageVandthespin-splitting?eldandspin-,suppressionofthespinimbalancesthatcanaffecttheusuallytheexpansionoftheFermi-Diracdistributionfunctioncanoef?cientsofsuperconductinghetero-bewrittenuptolinearterms,,thecalculatedspinSeebeckcoef?******@******@******@ffTdTeTeeVfTeTeeVte;exchange?eldandthechemicalpotential.******@******@emeasurementofchargeandspinSeebeckcoef?******@******@ffTtdTeTefTeTee;tothesuggestionofanewsetupofgraphene-basednano-struc-******@eturesincoolingapparatuses,thermalsensors,orevenrenew-***@f1?:(4)ableenergyapplications.***@,4kBTcosh2kBTwe?:InSo,urrentinEq.(1)canbedecoupledintotwoSubsectionIIIA,westudythethermoelectricpropertiesoftermsastheF-,thejunctionconsistingoftheRashbaspin-orbit(RSO)coupling,F-RSO-S,isdiscussedindTIchGVtIT:(5)?,?T;(6)supposedsystems,weimplementthegeneralizedBTKeTGrtGr-ferenttemperatures,thechargeandthermalcurrents?owinwhich,acrossthejunctionaseerNreTeGrIWGIT?ede;ch?deNeTe??feTefeTe:(1)2eIp2hKrLR4kBTcoshth2kBTe(7)Thesecurrentsdependontheelectric(G?GtG)andNreTeGrrrGr?de:thermal(K?KtK)conductances,inwhichrdenotes2err4kBTcoshthespindegreeoffreedomduetothepresenceof2kBT:..063903-,063903(2017)Now,weareabletocalculatethechargeandspin-–31However,inthecaseofdisorderedicsystemsbythefollow-graphene,thereisa?nitedensityofstatesthatappearsattheingequations:?eSrtSrT=2;Dependingonthenature,number,andsymmetryoftheSsp?SrSr:(8)impurities,,33Tocalculatethesecoef?cientsinoursupposedsystemsweToobtainthecarrier’swavefunctionsingraphene,wehetransmissionprobabilitiesviascat-usetheDirac-Bogoliubov-deGennes(DBdG)equation66,67teringprocesses.!!!Forapplicationsinthenano-scalecoolingdevices,itisHliDuuusefultoconsiderthe??i1?e;(11)DlT?H?Tvvspin-dependent?guresofmeritarede?nedbywhereTrepresentsthetime-?ch;theelectronandholepartsofwave-functions,(9)-SgraphenejunctionH?HZspT?;FicpartHF?eszr0Thforx0,superconductorpartHS?U0s0r0forx0wherejsp?jjrjrjisthespin-dependentthermalconduc-andthetwodimensionalDiracHamiltonianinonevalleyistivity,whereasGsp?jGrGrjisthespin-dependentcon-H?s,,the?,ponentsofthexystraightforwardalgebraaswavevectorinthexandydirections,,actingontherealspinandpseudo-spin2NreTeKrjr?ede:(10)2unitmatrices,andfor22e4kBTcoshsimplicityweassumehvF?,icexchange?,-Sjunctionturnstheexchange?eldtoagoodquantumnumberthatLetusconsideragraphene-basedF-Sjunction,whichisallowsforexplicitlyconsidering"-spinand#-spinquasi-par--spin-,-theDBdGequationintheFregion,eighteigenvaluesareicfeaturesareinducedinthegraphenelayerduetoobtained,,wesupposethatallsamplesarepure(.,q??????????????????????????e?6lF6ekFT2tekT26h:(12)disorder-free).ThecleangraphenelayerwithanextremelyxyhomogeneoussurfacecanbeproducedinexperimentusingTherefore,icexchange?eldalterstheorigi--valuesareF;626iae4T6ikF;exwe;"exT?e0;1;6e";0Tex;";F;66iae24T6ikF;exwe;#exT?e1;6e#;0;0Tex;#;hF;h(13)wF;6exT?e04;1;7e6ia";02TTe6ikx;"x;h;"F;6426iahT6ikF;hxwh;#exT?e0;0;1;7e#Tex;#;whereTisatransposeoperatorand0ndenotesa1-basedF--junctionissetinthex-ponentwavevector,k,inthescatteringprocesses,ductingregionsaresupposedsemi-in?"e#Tspin-upelectron