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

《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