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L.K.Shi,D.Zhang,L.B.Zhang,F.Cheng,W.K.Lou(IOS)S.C.ZhangDynamicsofGaussianPhys.Rev.B87,161115(R)(2013)LKS,SCZ,EffectiveGaugeFromtheHeisenbergusualgroup ProjectH0toElectronpositonEffectiveGaugeAdiabaticApproximation:Decouplingfast&slow Eeffetive whichisexactlyequaltotheBerryexactlytheBerryexactlytheBerryvelocityoperatortofirstorderinadiabaticBerryconstructingawavepacketusingtheBlochfunction,whichissharplydistributedinBrillouinzonevelocityforthecenter-of-massofthewavetheanomalousvelocitycausedbytheBerryEeffetive whichisexactlyequaltotheBerryNumerical yticalFasttremblingandorbitalSpin-upandspin-downelectronsbendtotheoppositeedges.Phys.Rev.B87,161115(R)(2013)LKS,SCZ,AnomalousElectronPhys.Rev.B87,161115(R)(2013)LKS,SCZ,MisakeyparameterM>0,Noedgestates!M<0,Edgestatesappear!Zitterbewegung:arelativisticquantumArapidtremblingmotionofForelectronobeyingDirac Thefrequencyofthistrembling

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