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ID:39120164
大小:1.11 MB
页数:41页
时间:2019-06-25
《二维三角晶格和kagome晶格上的紧束缚电子3a均匀与交错磁场下的量子Hall效应与Hofstadter能谱》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、1.●_●■1,,一‘,l●争ItITIGHT.BINDINGELECTRONSONTHETWo.DIMENSIONALTRIANGULARANDKAGOMELATTICESUNDERUNIFORMANDSTAGGEREDMoDULATEDMAGNETICFIELDSABSTRACT刀IequantumHalleffcctisoneofthemostspectacularphenomenaincondensedmaRerphysics.TheintegerquantumHalleffect(IQHE),discoveredb
2、yK.v.Klitzingetc.in1980isobservableinthesystemsofthetwo-dimensionalelectrongas,atlowtemperaturesandinthepresenceofastrongperpendicularmagneticfield.Later,thethephenomenologyofthe[QHEintheorywasexplainedbyR.B.Laughlinbasedonagauge-invarianceargument.Now,thequantized
3、Halleffectwasobservedinvariouslattices.111eelectronicpropertiesof2DperiodiclatticesimmersedinauniformmagneticfieldareofspecialinterestandhavebeenhottopicsofmanyphysicistssinceD.R.Hofstadterfoundtheenergyspectrumofthebutterflies。structuresforasquarelatticein1976.11他
4、essaywilldiscussthetight-bindingelectronicpeculiarpropertieson2Dtriangularandkagomelatticesundermagneticfields.Firstly,wefn'strevisitthebasicpropertiesofthetight-bindingelectronsontriangularandkagomelattices.Nexttheelectronicpropertiesisbydiscussedundertheauniform—
5、fluxpartwith咖andastaggered-fluxpartwithstrength△妒.Forconvenientanalysis,accordingtolatticesaretopologicallyequivalent,addedbondsbetweennext-nearest-neighborsitesofthesquarelatticeinonlyondirectiongetonenewtriangularlattice,andaddedsitesbetweennearest-neighborsitesa
6、ndlinkedthenewsiteswithbondsofthesquarelatticeinonlyonedirectiongetanothernewkagomelattice.WeadoptLandaugaugeandthecorresponding¨ABSTRACTperiodicalboundaryconditions(PBCs)forconvenientcalculation.Variouspropertiesof.■theHallconductanccsandtheHofstadterbutterfliesof
7、energyspectraaremainlystudied}bytheessay.When≯isfixed,variationof△咖leadstoquantumHalltransitionsandthe如jChemnumbersofLandausubbandsaleredistributedbetweenneighboringpairs.Theenergyspectraforthe2DtriangularlatticeandkagomelatticewithnonzeroA$’Shavesimilarfractalstru
8、cturesbutquitedifferentenergygapscomparedwinltheoriginalHofstadterbutterfliesof△≯=0.Moreover,thefan-likestructureofLandaulevelsatthelowmagneticfi
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