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1、Topologicalphasesingatedbilayergraphene:EffectsofRashbaspin-orbitcouplingandexchangefieldZhenhuaQiao,1XiaoLi,1Wang-KongTse,1HuaJiang,2YuguiYao,3andQianNiu1,21DepartmentofPhysics,TheUniversityofTexasatAustin,Austin,Texas78712,USA2InternationalCenterforQuantumMaterials,PekingUniversity,Beijing100871,Chi
2、na3SchoolofPhysics,BeijingInstituteofTechnology,Beijing100081,China(Dated:November19,2012)WepresentasystematicstudyontheinfluenceofRashbaspin-orbitcoupling,interlayerpotentialdifferenceandexchangefieldonthetopologicalpropertiesofbilayergraphene.InthepresenceofonlyRashbaspin-orbitcouplingandinterlayerpo
3、tentialdifference,thebandgapopeningduetobrokenout-of-planeinversionsymmetryoffersnewpossibilitiesofrealizingtunabletopologicalphasetransitionsbyvaryinganexternalgatevoltage.Wefindatwo-dimensionalZ2topologicalinsulatorphaseandaquantumvalleyHallphaseinAB-stackedbilayergrapheneandobtaintheireffectivelow-en
4、ergyHamiltoniansneartheDiracpoints.ForAAstacking,wedonotfindanytopologicalinsulatorphaseinthepresenceoflargeRashbaspin-orbitcoupling.Whentheexchangefieldisalsoturnedon,thebilayersystemexhibitsarichvarietyoftopologicalphasesincludingaquantumanomalousHallphase,andweobtainthephasediagramasafunctionoftheR
5、ashbaspin-orbitcoupling,interlayerpotentialdifference,andexchangefield.PACSnumbers:73.22.Pr,73.43.Cd,71.70.Ej,73.43.-fI.INTRODUCTIONplingstrengthsonthetopandbottomlayers(λ16=λ2),RRweshowthatthetopologicalinsulatorphaseremainsro-bustaslongasλ1λ2>t2.Whenthetime-reversalsym-Topologicalinsulator1(TI)isane
6、wphaseofquan-RR⊥tummatterinmaterialswithstrongspin-orbitcou-metryisbrokenbyanadditionalexchangefieldM,thepling.ThequantumspinHalleffectsingraphene2andbilayersystemhostsdifferenttopologicalphasescharac-HgTequantumwells3representthefirstexamplesoftwo-terizedbydifferentChernnumbersC=2,4sgn(M)anddimensionalt
7、opologicalinsulators.Sofar,semiconductorvalleyChernnumbersCv=2,4sgn(U),andthephaseheterostructureslikeHgTe5andInAs/GaSb6quantumboundariesassociatedwiththetopologicalphasetransi-tionsaregivenbyU=±MandU
