资源描述：
《Quantum Phase Transitions of Topological Insulators 》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、QuantumPhaseTransitionsofTopologicalInsulatorsLan-FengLiu1andSu-PengKou1,∗1DepartmentofPhysics,BeijingNormalUniversity,Beijing100875,China(Dated:January22,2010)Inthispaper,startingfromalatticemodeloftopologicalinsulators,westudythequantumphasetransitionsamongdifferen
2、tquantumstates,includingquantumspinHallstate,quantumanomalousHallstateandnormalbandinsulatorstatebycalculatingtheirtopologicalproperties(edgestates,quantizedspinHallconductiv-itiesandthenumberofzeromodeonaπ-flux).Wefindthatthereexistuniversalfeaturesforthetopologicalq
3、uantumphasetransitions(TQPTs)indifferentcases:theemergenceofnodalfermionsathighsymmetrypoints,thenon-analyticthirdderivativeofgroundstateenergyandthejumpsofthetopological”orderparame-ters”.Inparticular,therelationbetweenTQPTsandsymmetriesofthesystemsareexplored:differ
4、entTQPTsareprotectedbydifferent(global)symmetriesandthendescribedbydifferenttopological”orderparameters”.I.INTRODUCTIONAsthefirsttopologicallyorderedphase,theQuantumHallEffect(QHE)isaremarkableachievementincondensedmatterphysics1,2.InQHEstate,atlowtemperaturesandinstron
5、gmagneticfields,quantizedHallconductancecanbeobservedduetotheLandaulevelsformedbystatesofatwo-dimensionalelectrongas.Justoneyearlater,peoplediscoveredtheso-calledanomalousHalleffectwhereadditionalHallcurrentintheferromagneticmaterialarXiv:0909.5481v2[cond-mat.str-el]2
6、2Jan2010wasobserved3,4.Then,peoplefindthatthetransversetransportalsoexistsfordifferentspinspecies,whichiscalledasspinHalleffect5.Recently,thetopologicalinsulatorsincludingthequantizedspinHall(QSH)effect6–9andthequantizedanomalousHall(QAH)effect10,11becomehotissues.Ontheo
7、nehand,todescribethequantizedanomalousHallstate,aclassoftopologi-calinsulatorswithtime-reversalsymmetrybreaking,theChernnumber,socalledTKNN2integer,isintroducedasintegralsovertheBrillouinzone(BZ)oftheBerryfieldstrength12Z1Q=−(∇k×A)zdkxdky.(1)2πBZHereAj(k)=−ihuj
8、∇k
9、uj
10、iisaBerryconnectionforsingle-electronHamiltonianwiththeperiodicpartu(k)ofaBlochstateψ=u(k)eik·r.kOntheotherhand,forquantizedspinHallstatet
