高小红论文附录

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1、附录ABriefNoteontheFractionalQuantumHallEffectB.G.SidharthReceived:6April2014/Accepted:9December2014/Publishedonline:19February2015©SpringerScience+BusinessMediaNewYork2015Abstract:Weexplainfeaturesoftwodimensionalstructuresinapreciseway,intermsofthenon-commutativespacewhichdef

2、inesthesestructures.ThenovelfeaturehereisafundamentalexplanationfortheFQHE.Keywords:Hall-Eflcct・Quantum1TwoDimensionalConsiderationsTheQuantumHallEffectwasdiscoveredexperimentallyinthe1980s山.Inthiscase,asisbynowwellknown,foratwodimensionalsystemofelectrons,theHallconductivity

3、isfoundtobeoftheformG=ke2/h(1)whereXtakesonvaluesX=m/n(2)mandnbeingintegers.InparticularwehavethecasethatXisaninteger,calledtheintegralQuantumHallEffect囚Theimportantthingisthat(1)and(2)playaverypreciseroleinmetrology.Therehavebeenattemptstoexplainthisphenomenontheoreticallyin

4、particularbyinvokinggaugeinvariance卩].Howevertherehavebeensomepersistingpuzzles.WewillnowlookattheFractionalQuantumHallEffect(FQHE)fromacompletelynovelperspective,forexampleinthecaseofgraphene.Asiswellknowngrapheneisasinglelayergraphitewithmanyinterestingproperties.Someofthes

5、ehavebeenpredictedbytheauthorstarting1995[4~7^Theimportantpointhereisthatgraphenehasahoneycomblikelatticestructuresothatthespaceofgrapheneresemblesachessboardwith"holes'，inspaceitself[可Thismeansthatthereisafundamentalminimumlengthunderpinningthesystem.ThisfundamentallengthLle

6、adstoanon-commutativegeometry[9].ThiswaspointedoutalongtimeagointhecontextofQuantumElectrodynamics[10].Thismeansthatif(x,y)arethecoordinates,xy=yx.Indeed,aspointedout,graphenethereforeprovidesatestbedfortheseprinciplesofphysicswhichplayaroleinQuantumGravityapproaches・Insuchas

7、ituationithasbeenshownbytheauthorandindependentlySaitothatthereisastrongmagneticfield・Further,theauthorshowedthatthisfieldisgivenbyBL2=hc/e(3)L2definesaQuantumofareaexactlyasinQuantumGravityapproaches[14,15].Thisasiswellknownistheareaofindividuallattices,inourcase.Toelaborate

8、,theauthorhadarguedthat(3)holdsinthecaseofanoncommutativegeom・etry.T