Three-Dimensional Effects on the Electronic Structure of Quasiperiodic Systems

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1、FIMAT-8/95Three-dimensionaleffectsontheelectronicstructureofquasiperiodicsystemsEnriqueMaci´a∗andFranciscoDom´ınguez-AdameDepartamentodeF´ısicadeMateriales,FacultaddeF´ısicas,UniversidadComplutense,E-28040Madrid,SpainAbstractWereportonatheoreticlstudyoftheelectro

2、nicstructureofquasiperi-odic,quasi-one-dimensionalsystemswherefullythreedimensionalinteractionpotentialsaretakenintoaccount.Inourapproach,theactualphysicalpo-tentialactingupontheelectronsisreplacedbyasetofnonlocalseparablepotentials,leadingtoanexactlysolvableSch

3、r¨odingerequation.Bychoosinganappropriatetrialpotential,weobtainadiscretesetofalgebraicequationsthatcanbemappedontoageneraltight-binding-likeequation.WeintroducearXiv:cond-mat/9506107v123Jun1995aFibonaccisequenceeitherinthestrengthoftheon-sitepotentialsorinthene

4、arest-neighbordistances,andwefindnumericallythatthesesystemspresentahighlyfragmented,self-similarelectronicspectrum,whichbecomessingularcontinuousinthethermodynamicallimit.Inthiswayweextendtheresultsobtainedsofarinone-dimensionalmodelstothethree-dimensionalcase.A

5、sanexampleoftheapplicationofthemodelweconsiderthechain∗AlsoattheInstitutodeEstudiosInterdisciplinares,ElGuijo,Z4Galapagar,E-28260Madrid,Spain.1polymercase.TypesetusingREVTEX2I.INTRODUCTIONThestudyoftransportpropertiesofself-similaraperiodicstructureshasbeenacon-

6、tinuouslygrowingresearchfieldduringthelastdecade.Ontheoneside,theremarkablediscoveryofthequasicrystallinephase[1,2]gaverisetoaconsiderablyamountoftheoret-icalworkontransportpropertiesofFibonaccilattices,regardedasarchetypicalmodelsofquasiperiodicsystemsinonedimen

7、sion(1D)[3–9].Ontheotherside,sincethefirstgrowthofsemiconductingquasiperiodicsuperlattices[10,11],ithasbeenprogressivelyrealizedthatelectronicsystemsarrangedaccordingtoasubstitutionsequenceshouldofferinterestingpos-sibilitiesfortechnologicalapplications.Inaddition

8、,recentprogressesindiffusion-controlledaggregationonsurfaces,allowingtogrowth1Dchainsofatomsonasubstrate[12],alongwithproposalsofnanoscaledevicesbasedonatomicswitching