Where is the Luttinger liquid in one dimensional semiconductor quantum wire structures

We present the theoretical basis for analyzing resonant Raman scattering experiments in one-dimensional systems described by the Luttinger liquid fixed point. We make experimentally testable predictions for distinguishing Luttinger liquids from Fermi liqui

WhereistheLuttingerliquidinonedimensionalsemiconductorquantumwire

structures?

D.W.Wang(1),A.J.Millis(2),andS.DasSarma(1)

(1)DepartmentofPhysics,UniversityofMaryland,CollegePark,Maryland20742-4111

(2)CenterforMaterialsTheoryandDepartmentofPhysicsandAstronomy,RutgersUniversity,NewBrunswick,NewJersey

08554

(February6,2008)

WepresentthetheoreticalbasisforanalyzingresonantRamanscatteringexperimentsinone-dimensionalsystemsdescribedbytheLuttingerliquid xedpoint.WemakeexperimentallytestablepredictionsfordistinguishingLuttingerliquidsfromFermiliquidandarguethatpresentlyavailablequantumwiresystemsarenotintheregimewhereLuttingerliquide ectsareimportant.PACSnumbers:71.45.-d;73.20.Mf;73.20.Dx;78.30.Fs;78.30.-j.

arXiv:cond-mat/0004146v1 [cond-mat.str-el] 10 Apr 2000

Itistheoreticallywell-established[1-3]thataonedi-mensionalinteractingelectronsystem(1DES),isnotaFermiliquid(FL).UnlikeaFermiliquid,theinteract-ing1DEShasneithersharpfermionicquasiparticleexci-tationsnoradiscontinuityintheelectronmomentumdistributionfunction.Theelementaryexcitationsarechargee,spinzerobosonsandspin1/2charge0’semions’(fractionalstatisticsobjects),andthefermionisacom-positeofthese.Interacting1DEShavebeengenericallytermedLuttingerLiquids(LL)[2]andhavebeenthesub-jectofextensivetheoreticalstudyoverthelast40yearsandparticularlyoverthelastdecade.Despitetheintensetheoreticalinterest,therehavebeenfewconvincingex-perimentaldemonstrationsofthepredictedLLbehaviorinreal1DES.Thepower-lawdensityofstatesobservedintunnelingintoedgesofquantizedhallsystems[4]havebeeninterpretedintermsofthetheoreticallyexpected’chiralLuttingerliquid’behaviorofedgestates.Theori-ginofthedi erencesbetweentheobservedandexpectedexponentsispresentlyanareaofactiveinquiry.Pho-toemissionexperimentsonMottinsulatingoxideshavebeeninterpretedintermsofthe’holon’and’spinon’ex-citationsofachargedLuttingerliquid[5].

A1DESwhichisofparticularinterestbothforfunda-mentalphysicsandfortechnologyisthesystemformedinGaAs-basedsemiconductorquantumwire(QWR)struc-tures.Modernmaterialsgrowthandfabricationtech-niqueshaveproducednearlyideal1DESinwhichtheelectronmaymovefreelyonlyalongthelengthofthewire.Thetransversemotionisquantizedwiththequan-tum1DsubbandsseparatedbyseveralmeV.Itispos-sibletohavelowenoughcarrierdensitiessothatatlowtemperaturesonlythelowest1Dsubbandisoccupiedbyelectrons.SuchGaAsQWRbased1DESshouldbeidealsystemsforthestudyofinteractingelectronsinonedi-mensionbecausetheyarefreefromcomplicationsaris-ingfrombandstructure,latticee ects,andcrossoverstothreedimensionalbehaviorwhichoftenmakeinterpre-tationsofexperimentaldatadi cultinmoretraditional1DESbasedonorganiccompounds.

Itissurprising,therefore,thatnode nitiveLLbe-haviorhasbeenreportedinGaAsQWRsystems,andinfactthe1DFermigas/liquidmodelseemsto”work”operationallyverywellindescribingandexplainingtheobserved1DESexperimentalpropertiesinGaAsQWR[6,7].PartofthereasonfortheapparentabsenceoftheexpectedLLbehaviorisundoubtedlythefactthatinweaklyinteracting1DES,at nitetemperaturesandinthepresenceofimpurityscattering,theactualquantita-tivedi erencebetweenaLLandaFLisnotlarge[7],althoughthequalitativeconceptualdi erencebetweenthetwoishuge.Amorefundamentalissueisthatthedi erencesbetweenaLuttingerLiquidandaFermiliq-uidaremostobviousintheone-electronspectrum,whiletheexperimentalprobeswhichmaymostconvenientlybeappliedtotheQWRstructuresproduce’particle-holepairs’.Thedi erencesinparticle-holepairpropertiesbetweenLuttingerLiquidandFermiLiquidsystemsismuchlesspronouncedthanarethedi erencesintheoneelectronspectrum.ThisperhapsaccountsforthefactthatoneofthemostimportantprobesofQWRstruc-tures,resonantinelasticlightscatteringorRamanscat-teringspectroscopy(RRS)[6,8],hasnotyetobservedanyde nitiveindicationsofLLbehaviorinthesesystems.InRRSexperiments,lightisabsorbedatonefrequencyandre-emittedatanother,creatingoneormoreparticle-holepairs.Intheso-calledpolarizedgeometrywiththeincidentandoutgoingphotonshavingthesamepolariza-tion(sothatnospinistransferredtotheQWR),RRSexperimentsinGaAsQWRsconsistently[6,8]showtwopeakswhichindeedlookqualitativelyverysimilar[9]tothespectraforthecorresponding2Dand3Dsystems.Inthesehigherdimensionalsystems,thetwopeakshaveaclearandgenerallyacceptedFermiliquidinterpreta-tion[9].Thehigherenergypeakisassociatedwiththeplasmonorchargedensityexcitation(CDE),acollectivedensityexcitationoftheelectrongas,andtheloweren-ergyspectralpeakisassociatedwithincoherentparticle-holepairexcitations(SPE).IntheQWRmaterials,thelowerenergypeakoccursatan(approximate)excitationenergyof~qvF,whereqistheexcitationmomentumandvFisthe1DFermivelocityobtainedfromtheband

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