Glass Transition in a Two-Dimensional Electron System in Silicon
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arXiv:cond-mat/0212460v1 [cond-mat.str-el] 18 Dec 2002GlassTransitioninaTwo-DimensionalElectronSysteminSilicon
SneˇzanaBogdanovich,DraganaPopovi´cNationalHighMagneticFieldLaboratory,FloridaStateUniversity1800EastPaulDiracDrive,Tallahassee,FL32310,USA
1IntroductionThemetal-insulatortransition(MIT)intwodimensions(2D)hasbeenasub-jectofintensiveresearchinrecentyears[1]butthephysicsbehindthisphe-nomenonisstillnotunderstood.Ithasbeenestablished,however,thatitoccursintheregimewherebothCoulomb(electron-electron)interactionsanddisorderarestrong.Thecompetitionbetweenthesetwoeffectshasbeensug-gested[2]toleadtoglassydynamics(electronorCoulombglass).Therefore,ithasbeenproposedthatthe2DMITcanbedescribedalternativelyasthemeltingoftheWignerglass[3],orthemeltingoftheCoulombglass[4].Theex-istenceofalargenumberofmetastablestatesinaglassresultsinfluctuationsofconductivityσwithtime(conductivitynoise)sothatmesoscopicsamplesshouldbemoresuitableforstudiesofglassyproperties.Indeed,investiga-tionsofmetallicspinglasseshaveshown[5]thatmesoscopicmeasurementsarenecessaryinordertoprovidedetailedunderstandingofglassyorderinganddynamics.Herewereporttheresultsoftransportandnoisestudiesinmesoscopicsamples,whichdemonstrateforthefirsttimetheexistenceofaglassyphaseina2Dsysteminsemiconductorheterostructures.
2ExperimentThemeasurementswereperformedona1µmlong,90µmwiderectangularn-channelSimetal-oxide-semiconductorfield-effecttransistor(MOSFET)withthepeakmobilityofonly0.06m2/Vsat4.2K.Othersampledetailshavebeengivenelsewhere[6].ThefluctuationsofcurrentI(i.e.σ)asafunctionoftimeweremeasuredusingalow-noisecurrentpreamplifierandastandardtwo-probelock-intechniqueat∼13HzwiththeconstantexcitationvoltageVexc∼afewµV.BychangingthegatevoltageVg,theelectrondensityns
wasvariedbetween3.4×1011cm−2and20.2×1011cm−2,whereastemperature
Trangedbetween0.13Kand0.80K.Itwasestablishedthatthecurrentfluctuationswerenotcorrelatedwith(i.e.notdueto)thefluctuationsoftemperatureorappliedvoltage.Inaddition,anothersamplefromthesamewaferwasmeasuredinafour-terminalconfigurationat0.25K,anditwasdeterminedthatthecontactresistancesandthecontactnoisewerenegligible.
3ResultsFig.1(left)showsthetimedependenceoftherelativefluctuations(σ−σ)/σ(where...denotesaveragingovertime)forafixednsatdiffer-entT.AtthelowestT=0.13K,fluctuationsareashighas250%,anddroprapidlywithincreasingT.Asimilardecreaseinfluctuationswasobservedwithincreasingns,asdiscussedinmoredetailbelow.
Thetime-averagedconductivityσwascalculatedfortimeintervalsofsev-eralhours,forallnsandT.Fig.1(right)depictsσasafunctionofTatselectedns.Similartothebehaviorofvarioushigh-mobility2Dsystems[1],thetemperaturecoefficientofconductivitydσ/dTchangessignwhenσ(n∗s)=0.5e2/h.Eventhoughthecorrespondingdensityn∗s=12.9×1011cm−2ismuchhigherduetoalargeamountofdisorderinoursamples,theeffectiveCoulombinteractionisstillcomparabletothatinother2Dsystems(rs=4.6,rs–ratioofCoulombenergytoFermienergy).Thedensitiesn∗s,wheredσ/dT=0,havebeenusually[1]identifiedwiththecriticaldensityncforthemetal-insulatortransition.However,athoroughanalysisofσ(ns,T)atlowns
shows[6]that,inourcase,nc=(5.0±0.3)×1011cm−2,whichismorethana
2factoroftwosmallerthann∗s.Thedifferencebetweenncandn∗sinoursamplesisattributedtoalargeramountofdisorder.
Theroot-mean-square(rms)fluctuationsδσ=(σ−σ)21/2(calculatedoverthefrequencybandwidthfrom(10hours)−1to(6seconds)−1)increasewithns,rangingbetween(10−5−10−2)e2/hatallT.Fig.2(left)showstherelativerms,δσ/σ,asafunctionofnsatthreedifferentT.Whilefluctuationsseemtobeindependentofdensityathighns,adramaticincreaseofδσ/σisobservedwithdecreasingnsbelowng=(7.5±0.3)×1011cm−2.EventhoughanincreaseinTcausesasubstantialreductionofδσ/σ,theonsetoflargefluctuationsdoesnotseemtodependontemperature.
ThenoisewasstudiedinmoredetailusingnormalizedpowerspectraSI(f)=S(I,f)/I2,mostofwhichwereobtainedinthef=10−4−10−1Hzbandwidth.Theywerefoundtofollowthewell-knownpower-lawfrequencydependenceSI∝1/fα(Hooge’slaw)[7].Inallmeasurements,thedevicenoisewasex-tractedfromthetotalmeasurednoisebysubtractingthebackgroundnoisepresentwithnocurrentflowing,i.e.bysettingVexc=0.Thepowerspectrumofthebackgroundnoisewasalwaysseveralordersofmagnitudesmallerthansamplenoiseandhadnof-dependence(whitenoise).Fig.2(center)showsSI
asafunctionofnsatf=3.16×10−4HzandT=0.13K.Athighns,SIdoes
notdependonnswithinthescatterofdata.FornsnentialriseofSIbysixordersofmagnitudeisobservedwithdecreasingns.Thisstrikingincreaseoftheslowdynamiccontributiontoσisconsistentwiththebehaviorofδσ/σ(Fig.2,left).Infact,since(δσ)2/σ2=SI(f)df,itisclearthattheobservedenormousincreaseoftherelativermsasnsisre-ducedbelowng(Fig.2,left)reflectsadramaticslowingdownoftheelectrondynamics.Thisisattributedtothefreezingoftheelectronglass.