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1、REVIEWSOFMODERNPHYSICS,VOLUME81,JANUARY–MARCH2009TheelectronicpropertiesofgrapheneA.H.CastroNetoDepartmentofPhysics,BostonUniversity,590CommonwealthAvenue,Boston,Massachusetts02215,USAF.GuineaInstitutodeCienciadeMaterialesdeMadrid,CSIC,Cantoblanco,E-28049Madrid,SpainN.M.R.Peres
2、CenterofPhysicsandDepartmentofPhysics,UniversidadedoMinho,P-4710-057,Braga,PortugalK.S.NovoselovandA.K.GeimDepartmentofPhysicsandAstronomy,UniversityofManchester,Manchester,M139PL,UnitedKingdomPublished14January2009Thisarticlereviewsthebasictheoreticalaspectsofgraphene,aone-a
3、tom-thickallotropeofcarbon,withunusualtwo-dimensionalDirac-likeelectronicexcitations.TheDiracelectronscanbecontrolledbyapplicationofexternalelectricandmagneticÞelds,orbyalteringsamplegeometryand/ortopology.TheDiracelectronsbehaveinunusualwaysintunneling,conÞnement,andtheinteger
4、quantumHalleffect.Theelectronicpropertiesofgraphenestacksarediscussedandvarywithstackingorderandnumberoflayers.Edgesurfacestatesingraphenedependontheedgeterminationzigzagorarmchairandaffectthephysicalpropertiesofnanoribbons.DifferenttypesofdisordermodifytheDiracequationlead
5、ingtounusualspectroscopicandtransportproperties.Theeffectsofelectron-electronandelectron-phononinteractionsinsinglelayerandmultilayergraphenearealsopresented.DOI:10.1103/RevModPhys.81.109PACSnumbers:81.05.Uw,73.20.r,03.65.Pm,82.45.MpCONTENTSB.Topologicallatticedefects136C.Im
6、puritystates137D.Localizedstatesnearedges,cracks,andvoids137I.Introduction110II.ElementaryElectronicPropertiesofGraphene112E.Self-doping138A.Singlelayer:Tight-bindingapproach112F.VectorpotentialandgaugeÞelddisorder1391.Cyclotronmass1131.GaugeÞeldinducedbycurvature1402.Densityof
7、states1142.Elasticstrain140B.Diracfermions1143.RandomgaugeÞelds1411.ChiraltunnelingandKleinparadox115G.Couplingtomagneticimpurities1412.ConÞnementandZitterbewegung117H.Weakandstronglocalization142C.Bilayergraphene:Tight-bindingapproach118I.TransportneartheDiracpoint143D.Epitaxi
8、algraphene119J.Boltzmannequationdescriptionofdctranspo
