Clustering-by-fast-search-and-find-of-density-peak

DOI:10.1126/science.1242072,1492(2014);344ScienceAlexRodriguezandAlessandroLaioClusteringbyfastsearchandfindofdensitypeaksThiscopyisforyourpersonal,non-commercialuseonly.clickinghere.colleagues,clients,orcustomersby,youcanorderhigh-qualitycopiesforyourIfyouwishtodistributethisarticletoothers here.followingtheguidelinescanbeobtainedbyPermissiontorepublishorrepurposearticlesorportionsofarticles ):June29,2014(thisinformationiscurrentasofThefollowingresourcesrelatedtothisarticleareavailableonlineat:includinghigh-resolutionfigures,canbefoundintheonlineUpdatedinformationandservices,:SupportingOnlineMaterial:cites14articlesThisarticle:ThisarticleappearsinthefollowingregisteredtrademarkofAAAS.isaScience2014bytheAmericanAssociationfortheAdvancementofScience;allrightsreserved.ThetitleCopyrightAmericanAssociationfortheAdvancementofScience,1200NewYorkAvenueNW,Washington,DC20005.(printISSN0036-8075;onlineISSN1095-9203)ispublishedweekly,exceptthelastweekinDecember,bytheScienceonJune30,2014(suchasthedopingdensityandtheamountofdisorder).Studiesofthede-pendenceontemperatureandondisorderarethereforerequiredtobetterunderstandthedopingdensitydependenceoftheVHE.Furthermore,amoreaccuratedeterminationofsHthattakesintoaccountthefringefieldsinourHallbardevicemaybeneededforabetterquantitativecomparison.REFERENCESANDNOTES1.A.H.CastroNeto,F.Guinea,N.M.R.Peres,K.S.Novoselov,A.K.Geim,Rev.Mod.Phys.81,109–162(2009).2.A.Rycerz,J.Tworzydlo,C.W.J.Beenakker,Nat.Phys.3,172–175(2007).3.A.R.Akhmerov,C.W.J.Beenakker,Phys.Rev.Lett.98,157003(2007).4.D.Xiao,W.Yao,Q.Niu,Phys.Rev.Lett.99,236809(2007).5.W.Yao,D.Xiao,Q.Niu,Phys.Rev.B77,235406(2008).6.D.Xiao,G.-B.Liu,W.Feng,X.Xu,W.Yao,Phys.Rev.Lett.108,196802(2012).7.Y.J.Zhang,T.Oka,R.Suzuki,J.T.Ye,Y.Iwasa,Science344,725–728(2014).8.K.F.Mak,C.Lee,J.Hone,J.Shan,T.F.Heinz,Phys.Rev.Lett.105,136805(2010).9.A.Splendianietal.,NanoLett.10,1271–1275(2010).10.T.Caoetal.,Nat.Commun.3,887(2012).11.K.F.Mak,K.He,J.Shan,T.F.Heinz,Nat.Nanotechnol.7,494–498(2012).12.G.Sallenetal.,Phys.Rev.B86,081301(2012).13.S.Wuetal.,Nat.Phys.9,149–153(2013).14.H.Zeng,J.Dai,W.Yao,D.Xiao,X.Cui,Nat.Nanotechnol.7,490–493(2012).15.D.Xiao,M.-C.Chang,Q.Niu,Rev.Mod.Phys.82,1959–2007(2010).16.X.Li,F.Zhang,Q.Niu,Phys.Rev.Lett.110,066803(2013).17.S.Murakami,N.Nagaosa,S.-C.Zhang,Science301,1348–1351(2003).18.J.Sinovaetal.,Phys.Rev.Lett.92,126603(2004).19.Y.K.Kato,R.C.Myers,A.C.Gossard,D.D.Awschalom,Science306,1910–1913(2004).20.J.Wunderlich,B.Kaestner,J.Sinova,T.Jungwirth,Phys.Rev.Lett.94,047204(2005).21.J.Wunderlichetal.,Science330,1801–1804(2010).22.N.Nagaosa,J.Sinova,S.Onoda,A.H.MacDonald,N.P.Ong,Rev.Mod.Phys.82,1539–1592(2010).23.MaterialsandmethodsareavailableassupplementarymaterialsonScienceOnline.24.Theskewscatteringcontribution,whichisimportantonlyforhigh-mobilitydevices(22),isneglectedinMoS2deviceswithrelativelylowmobility.25.T.Cheiwchanchamnangij,W.R.L.Lambrecht,Phys.Rev.B85,205302(2012).26.B.Radisavljevic,A.Radenovic,J.Brivio,V.Giacometti,A.Kis,Nat.Nanotechnol.6,147–150(2011).27.L.J.vanderPauw,PhilipsTechn.Rev.20,220–224(1958).28.B.W.H.Baugher,H.O.H.Churchill,Y.Yang,P.Jarillo-Herrero,NanoLett.13,4212–4216(2013).29.G.Kioseoglouetal.,Appl.Phys.Lett.101,221907(2012).30.O.Lopez-Sanchez,D.Lembke,M.Kayci,A.Radenovic,A.Kis,Nat.Nanotechnol.8,497–501(2013).31.Strictlyspeaking,abilayerdevicewithslightlybrokeninversionsymmetrybythesubstrateand/orbyunintentionaldopingcouldalsoproduceafiniteVHE,buttheseeffectsareexpectedtobemuchsmallerascomparedwiththeVHEinmonolayerdevices(13).32.Here,ourassumptionthatonlythephotoexcitedelectronscontributetotheHallresponseisreasonablebecausetheholesaremuchmorevulnerabletotrapsthanaretheelectrons,givenourhighlyn-dopeddevice.Unliketheelectronside,theVHEandtheSHEbecomeequivalentontheholesideowingtothespin-valleycoupledvalenceband.33.H.-A.Engel,B.I.Halperin,E.I.Rashba,Phys.Rev.Lett.95,166605(2005).ACKNOWLEDGMENTSWethankD.C.RalphforhisinsightfulsuggestionsandJ.W.Kevekfortechnicalsupport.WealsothankJ.ShanformanyfruitfuldiscussionsandY.YouforprivatecommunicationsregardingtheopticaldataonmonolayerMoS2.ThisresearchwassupportedbytheKavliInstituteatCornellforNanoscaleScienceandtheCornellCenterforMaterialsResearch[NationalScienceFoundation(NSF)DMR-1120296].AdditionalfundingwasprovidedbytheAirForceOfficeofScientificResearch(FA9550-10-1-0410)andtheNano-Material