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1、REVIEWSOFMODERNPHYSICS,VOLUME82,JULY–SEPTEMBER2010BerryphaseeffectsonelectronicpropertiesDiXiaoMaterialsScienceandTechnologyDivision,OakRidgeNationalLaboratory,OakRidge,Tennessee37831,USAMing-CheChangDepartmentofPhysics,NationalTaiwanNormalUniversity,Taipe
2、i11677,TaiwanQianNiuDepartmentofPhysics,TheUniversityofTexasatAustin,Austin,Texas78712,USAPublished6July2010EversinceitsdiscoverythenotionofBerryphasehaspermeatedthroughallbranchesofphysics.OverthepastthreedecadesitwasgraduallyrealizedthattheBerryphaseof
3、theelectronicwavefunctioncanhaveaprofoundeffectonmaterialpropertiesandisresponsibleforaspectrumofphenomena,suchaspolarization,orbitalmagnetism,variousquantum,anomalous,orspinHalleffects,andquantumchargepumping.Thisprogressissummarizedinapedagogicalmanner
4、inthisreview.AbriefsummaryofnecessarybackgroundisgivenandadetaileddiscussionoftheBerryphaseeffectinavarietyofsolid-stateapplications.Acommonthreadofthereviewisthesemiclassicalformulationofelectrondynamics,whichisaversatiletoolinthestudyofelectrondynamicsin
5、thepresenceofelectromagneticÞeldsandmoregeneralperturbations.Finally,arequantizationmethodisdemonstratedthatconvertsasemiclassicaltheorytoaneffectivequantumtheory.ItisclearthattheBerryphaseshouldbeaddedasanessentialingredienttoourunderstandingofbasicmateri
6、alproperties.DOI:10.1103/RevModPhys.82.1959PACSnumbers:71.70.Ej,72.10.Bg,73.43.f,77.84.sCONTENTSB.Orbitalmagnetization1978C.Dipolemoment1979D.Anomalousthermoelectrictransport1980I.Introduction1960V.ElectronDynamicsinElectromagneticFields1980A.Topicalov
7、erview1960A.Equationsofmotion1981B.Organizationofthereview1961B.ModiÞeddensityofstates1981C.BasicconceptsoftheBerryphase19621.Fermivolume19821.Cyclicadiabaticevolution19622.Stredaformula19822.Berrycurvature1963C.Orbitalmagnetization:Revisit19823.Example:Th
8、etwo-levelsystem1964D.Magnetotransport1983D.BerryphaseinBlochbands19651.Cyclotronperiod1983II.AdiabaticTransportandElectricPolarization19662.Thehigh-Þeldlimit1984A.Adiabaticcurrent19663.Thelow-Þeldlimit1984B.
