Electron-electron interaction in graphene

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1、Electron-electroninteractioningraphenePhilipKimDepartmentofPhysicsColumbiaUniversitySplittingofLandauLevelsinHighMagneticFields22xy=-Rxy/(Rxy+Rxx)Lowfields(B<10T)9T1.6K25T=2,6,10,….+_+_+_Mobility~20,000cm2/VSec30T37T42THighfields(B>20T)45T=0,+_1,2,+_+_4,6,…+_LandauLevel=6=4energy=2=1=0=-

2、1=-2=-4=-6BY.Zhangetal.,PRL(2006)Spin&valleysymmetrylifted!Howtobreaksub-latticesymmetry?SpontaneousSymmetryBreakingChargedensitywave,Spindensitywave,Skyrmions,excitons,andetcTheoryReferencelist(partial)SU(4)Symmetry:spin/pseudospinQuantumHallInsulatorORQuantumHallFerromagnet?LowmagneticfieldH

3、ighmagneticfielddegeneracybreak:twoscenariosQHEFerromagnetQHEInsulatorn=3Spin->PseudoSpinPseudoSpin->Spinn=2n=1n=0LandauLevelEnergyDOSn=-1n=-2BBn=-3xxSpin&Pseudo-spindegenerateQHedgestatesQHedgestatesNormura&Macdonald,PRL96,256602(2006);Abanin,Lee,&Levitov,PRL98,156801(2007);ResistanceMaximumfo

4、r=0QuantumHallState30TAbanin,etal.,Phys.Rev.Lett.98,196806(2007)J.Chekelsky,L.Li,N.P.Ong,PRL(2007)PRB(2008)MetallictemperaturebehaviorInsulatorlikebehaviorsforcleansamples<40k@30Tathighmagneticfield30T.xxTransportGapMeasurementattheDiracPointCorbinoMeasurementHallBarMeasurementVbiasIIIVxxInth

5、eQuantumHallregimexx=I/Vbias=0IntheQuantumHallregimeFillingfactorGrapheneCorbino=0:R=V/I=0xxxx•Dielectriclayerdeposition•Contactviafabrication=0:R=0xx•Innerelectrode(ifscatteringhappens…)10mcontactedbyagroundplaneQuantumHallEffectinGrapheneCorbinoDevice220-10-6-202=0T=0)/hxxTemperatureDepe

6、ndent2e(110(e2xx/h0.8)1.50K31T1.83K0.62.53K3.70K/h)4.98K200(e12.12K0.4-80-4004080xxVg(V)0.2T=1.5K10mMobility~10,000cm2/Vsec0.0010203040V(V)gTransportGapin=0stateActivationEnergyGapat31TMagneticFieldDependence119T1.50KT=1.5K1.022T1.83K25T2.53K28T0.13.70K31.13T4.98K/h)12.12K2/h)(e0.520.01xx(e

7、xx1E-30.0-0.4-0.20.00.20.41E-4(V-V)/B(V/T)gdirac010203040106V(V)griova13)eh105bg(tinalt)12sumaxnimaxxxedxxR104ucdR11inldln(ieF10E~10.5K103act15202530350.00.20.40.60.8B(T)1/TSimilartoJ.Chekelsky,L.Li,N.P.Ong,PRL(2007