Transport in a one-dimensional Luttinger liquid

In this paper we review recent theoretical results for transport in a one-dimensional (1d) Luttinger liquid. For simplicity, we ignore electron spin, and focus exclusively on the case of a single-mode. Moreover, we consider only the effects of a single (or

Transportinaone-dimensionalLuttingerliquid

1

MatthewP.A.Fisher1andLeonidI.Glazman2

InstituteforTheoreticalPhysics,UniversityofCalifornia,SantaBarbara,CA93106–4030

2

TheoreticalPhysicsInstitute,UniversityofMinnesota,Minneapolis,MN55455

(February1,2008)

arXiv:cond-mat/9610037v1 [cond-mat.mes-hall] 6 Oct 1996

Inthispaperwereviewrecenttheoreticalresultsfortransportinaone-dimensional(1d)Luttingerliquid.Forsimplicity,weignoreelectronspin,andfocusexclusivelyonthecaseofasingle-mode.Moreover,weconsideronlythee ectsofasingle(orperhapsseveral)spatiallylocalizedimpurities.Evenwiththeserestrictions,thepredictedbehaviorisveryrich,andstrikinglydi erentthanfora1dnon-interactingelectrongas.Themethodofbosonizationisreviewed,withanemphasisonphysicalmotivation,ratherthanmathematicalrigor.Transportthroughasingleimpurityisreviewedfromseveraldi erentperspectives,asapinnedstronglyinteracting“Wigner”crystalandinthelimitofweakinteractions.Theexistenceoffractionallychargedquasiparticlesisalsorevealed.Inter-edgetunnellinginthequantumHalle ect,andcharge uctuationsinaquantumdotundertheconditionsofCoulombblockadeareconsideredasexamplesofthedevelopedtechniques.

I.INTRODUCTION

Landau’sFermiliquidtheoryisabeautifulandsuc-cessfultheorywhichaccountsforthebehaviorofcon-ductionelectronsinconventionalmetallicsystems.Thecentralassumptionofthistheory,isthatthelowenergyexcitedstatesoftheinteractingelectrongascanbeclas-si edinthesamewayasareferencenon-interactingelec-trongas.Uponadiabatically“switchingon”theelectroninteractions,theexcitedstatesarestillcomposedoffreequasiparticles,labelledbymomentum,whichobeyFermistatistics.Thelowenergyexcitationsabovethegroundstate,consistofcreatingquasiparticles(andquasiholes)withmomentajustabove(below)theFermisurface.Thesingle-particlespectralfunctionforanelectronispre-sumedtohaveaδ-functionpeakattheFermisurface,A(kF, )=2πZFδ( ),withanon-zerocoe cient,ZF.Forthenon-interactingelectrongasZF=1,butwithinteractionsZF<1,re ectingasmalleroverlapbetweentheelectronandthequasiparticle.However,providedZFisnon-zero,thereexistwellde nedlowenergyquasi-particleexcitations,whichareinaone-to-onecorrespon-dencewiththebareelectronexcitationsofthereferencenon-interactingelectrongas.ItisthenpossibletobuildatransporttheoryofFermiliquidsindirectanalogywithDrudetheoryofthefreeelectrongas,byfocussingonthescattering(byimpurities,say)ofthelowenergyquasipar-ticleexcitations.Forexample,aquasiparticlewillscattero animpuritywitha nitecross-section,leadingtoametallicresisitivityforlowimpurityconcentration.

Foraweakly-interactingelectrongas,deviationsinthespectralweightZFfromonecanbecomputedperturba-tivelyintheinteractionstrength,providedthespatialdimensionality,d,isgreaterthanone.However,fortheone-dimensionalinteractingsystem,lowordertermsintheperturbationtheoryaredivergent.ThissignalsthebreakdownofLandau’sFermiliquidtheoryinthe1delec-trongas,forarbitrarilyweakinteractions2.Thisdiver-1

gencecanbetracedtothelargephasespacein1d,foranelectrontorelaxbycreatinganelectron-holeexcitation.Ford>1,bothenergyandmomentumconservationhighlyconstraintheavailablephasespace,butin1dforasinglebranchwithlineardispersion,momentumcon-servationautomaticallyimpliesenergyconservation,sothephasespaceislessconstrained.Thisleadstoadiver-gentrateforsuchscatteringprocesses,andtheelectronbecomes“dressed”byalargenumberofelectron-holepairs.Thisinturndrivestheelectronspectralweighttozero,ZF=0,evenforweakelectroninteractions.Inthelimitofweakinteraction,itisstillpossibletoextracttheresultingpropertiesofthe1delectrongasbyacleverre-summationofthemostdivergenttermsineachorderofperturbationtheory3However,thephysicsismoreread-ilyrevealedbythemethodofbosonization,asdiscussedbelow.

Tomonaga4(andmorerecentlyLuttinger5)consideredaspecialclassofinteracting1delectronmodels,whichwerelinearizedaroundtheFermipoints,andcouldbedi-agonalizedintermsofbosonvariables.Thesebosonvari-ablesdescribedcollectiveplasmonexcitations,ordensitywaves,intheelectrongas.Someyearslater,Haldane6ar-guedthatthisbosonizeddecriptionwasvalidmoregener-ally,givinganappropriatedescriptionforthelowenergyexcitationsofageneric1dinteractingelectrongas.Hal-danecoinedtheterm“Luttingerliquid”todescribethisgenericbehavior,althoughsometimesitisreferredtoasaTomonaga-Luttingerliquid.Insucha1dLuttingerliq-uid,creationofarealelectronisachievedbyexcitinganin nitenumberofplasmons.Becauseofthis,thespaceandtimedependenceoftheelectroncorrelationfunctionisdramaticallydi erentthaninanon-interactingelec-trongas,orinaFermiliquid7.Thismanifestsitselfinvariouskineticquantities,inparticulartheDrudecon-ductivity,whichistovary(asapowerlaw)withtemperature8–10.TheLuttingerliquidapproachtotransportin1dsystemswaspopularinthe1970‘s,be-

Word文档免费下载Word文档免费下载:Transport in a one-dimensional Luttinger liquid (共20页,当前第1页)

Transport in a one dimensional Luttinger liquid相关文档

最新文档

返回顶部