Comment on cond-mat0409228 Microwave photoresponse in the 2D electron system caused by intr

We provide an article-extract which points out that a microwave-induced modification in the resistance occurs at relatively "high" magnetic fields where the radiation is incapable of producing inter-Landau level excitations and, therefore, that the microwa

Commentoncond-mat/0409228”Microwavephotoresponseinthe2Delectronsystem

causedbyintra-Landauleveltransitions”

R.G.Mani1,

1

2004

HarvardUniversity,GordonMcKayLaboratoryofAppliedScience,9OxfordStreet,Cambridge,MA02138,USA

(Dated:February2,2008)

Weprovideanarticle-extractwhichpointsoutthatamicrowave-inducedmodi cationintheresistanceoccursatrelatively”high”magnetic eldswheretheradiationisincapableofproducinginter-Landaulevelexcitationsand,therefore,thatthemicrowaveradiationmustbeproducingintra tcLandaulevelexcitationsaswell.

O 9Intheabovementionedcond-matpreprintentitled ”Microwavephotoresponseinthe2Delectronsystem]lcausedbyintra-Landauleveltransitions”,Dorozhkinetlaal.[1]havediscussedaregimeofthemicrowave-inducedhresponseinthe2DESthatdoesnotobtainmuchatten--stion-thelimitof”high”magnetic elds,B,wheretheeLandaulevelspacingh¯ωcexceedsthephotonenergyhf.mBasedontheavailablemodelsforthemicrowave-induced.magnetoresistance,[2]onenaivelyexpectslittlechangeintathemagnetoresistanceuponmicrowaveexcitationinthismlimitbecauseinterLandaulevelexcitationsduetosin--glephotonprocessesareenergeticallyunfavorableanddunlikelywhenB>Bnf,i.e.,h¯ωC>hf.Here,Bf=

o2πfm

/e,fisthemicrowavefrequency,m isane ec-ctivemass,andeistheelectroncharge.Thus,thisB>[ Bfregimeisnoteworthybecauseitpointsoutfurther 1complexityintheexperimentallyobservedphenomena,vthanwhathasbeenappreciatedthusfar.

7Incond-mat/0409228,[1]theclaimtonoveltyseemsto2bethattheworkrepresentsthe rstconsciousidenti -2cationofaroleforintraLandauleveltransitionsinthe01microwaveinducedresistanceresponseintheB>Bf4limit.

0Anidenti cationofaroleforintraLandauleveltransi-/ttionsinthemicrowaveinducedmagnetoresistanceintheaB>Bmflimithasbeenmadepreviously,however,atthe13thInternationalWinterschoolonNewDevelopments-dinSolidStatePhysics-LowDimensionalSystems,innMauterndorf(Salzburg),Austria.[3]Anextractfromtheassociatedpaper,wherethemicrowaveinducedmagne-cotoresistanceintheB>Bflimithasbeenattributedto:vspin- ipintraLandaulevelexcitations,isprovidedintheiXfollowingtwopages.[3]

Perhaps,spin- ipintraLandaulevelexcitationsmightraconstituteaviablemechanismforunderstandingtheobservedphoto-inducedmagnetoresistancee ectintheB>Bflimit.[3]Certainly,spin- ipintraLandaulevelexcitationsremainenergeticallyplausibleintheB>Bflimit,thespinsplittingincludesaBvariationdueto

the eldinducedZeemanterm,and,themagnitudeofthespin-splitting,uponincludingspin-orbite ects,liesinthefrequency(energy)range,[4]wherethemicrowaveradiationproducesaresistancereduction.[3,5]

Electronicaddress:mani@deas.harvard.edu[1]S.Dorozhkinetal.,cond-mat/0409228.

[2]

V.I.Ryzhii,Sov.Phys.-Sol.St.11,2078(1970);J.C.Phillips,m.127,233(2003);A.C.Durstetal.,Phys.Rev.Lett.91,086803(2003);A.V.Andreevetal.,Phys.Rev.Lett.91,056803(2003);J.ShiandX.C.Xie,Phys.Rev.Lett.91,086801(2003);F.S.Bergeretetal.,Phys.Rev.B67,241303(2003);A.A.KoulakovandM.E.Raikh,Phys.Rev.B68,115324(2003);V.RyzhiiandR.Suris,J.Phys.Condens.Mat.15,6855(2003);X.L.LeiandS.Y.Liu,Phys.Rev.Lett.91,226805(2003);I.A.Dmitrievetal.,Phys.Rev.Lett.91,226802(2003);cond-mat/0310668;V.RyzhiiandA.Satou,J.Phys.Soc.Jpn.72,2718(2003);M.G.VavilovandI.L.Aleiner,Phys.Rev.B69,035303(2004);A.F.VolkovandV.V.Pavlovskii,Phys.Rev.B69,125305(2004).

[3]

R.G.Mani,intheProceedingsofthe13thInternationalWinterschoolonNewDevelopmentsinSolidStatePhysics-LowDimensionalSystems,editedbyG.Bauer,W.Jantsch,andF.Kuchar(Mauterndorf(Salzburg),Austria,16-20February,2004)[PhysicaE(Amsterdam)(availableonline/29July2004)].

[4]Y.A.BychkovandE.IRashba,JPhys.C.17,6039(1984);G.Dresselhaus,Phys.Rev.100,580(1955);E.A.DeAndradaeSilvaetal.,Phys.Rev.B50,8523(1994).[5]

Theargumenthasbeenmadethatspin-e ectsneednotbeconsideredherebecause”spin-splittingisnotresolved.”[1]Yet,itisnotobviousthatspin-splittingneedstobe”resolved”forspintohaveaperceptiblee ectontheradiation-inducedmagnetoresistance.Certainly,experi-menthasalreadyshownaradiation-inducedmagnetore-sistancee ect(forB<Bf)evenwhereLandaulevelsplit-tingisapparently”unresolved”byexperiment,i.e.,whereSdHoscillationsarenotobservable,see,forexample,Fig.3(a)inR.G.Manietal.,Phys.Rev.Lett.92,146801(2004).

We provide an article-extract which points out that a microwave-induced modification in the resistance occurs at relatively "high" magnetic fields where the radiation is incapable of producing inter-Landau level excitations and, therefore, that the microwa

ARTICLEINPRESS

R.G.Mani/PhysicaE](]]]])]]]–]]]

3

illustratedbyFigs.3

and4.Atthelowestfrequency,f¼3:35GHz;seeFig.3(a),regularoscillationsdonotappearinRxx;andthemicrowaveradiationseemstoproducemostlynegativemagnetoresistance,suchthattheirra-diatedRxxfallsbelowthedarkRxxat eldswellaboveBf:At eldsaboveBf;theradiationseemsincapableofproducinginter-Landaulevelexcita-tions,andtherefore,anewmechanismappearsnecessarytodescribethislow-fbehavior.AstheradiationenergyattheappliedfinFig.3(a)seems

1.5

1.0)

( xxR0.5

0.0(a)

2.0

1.5

)

( xx1.0

R0.5

0.0Bf (15.6 GHz)

(b)

B (T)

Fig.3.This gureexhibitstheeffectofmicrowaveirradiationonthediagonalresistance,Rxx;atrelativelylowmicrowavefrequencies.(a)Atf¼3:35GHz;theradiationmostlypro-ducesnegativemagnetoresistanceatmagnetic eldswellaboveBf;wheretheradiationseemsincapableofproducinginter-Landaulevelexcitations.(b)Withincreasingf;theradiation-inducedreductioninRxxaboveBfbecomeslesspronouncedasaresistancemaximum,the‘‘ rstresistancemaximum,’’becomesperceptible.

tolieinthevicinityoftheexpectedzero- eldspinsplittingduetotheRashbaandDresselhaustermsinthisGaAs/AlGaAssystem[19],wesuggestthattheobservedlowfbehaviormightre ectradia-tion-inducedmixingbetweenspinlevelsofthesameLandauband,andthemodi cationofthismixing,duetothe eld-inducedZeemanterm.Theeffectofincreasingf;atrelativelylowf;isexhibitedinFig.3(b).Here,oneobservesthatasf

We provide an article-extract which points out that a microwave-induced modification in the resistance occurs at relatively "high" magnetic fields where the radiation is incapable of producing inter-Landau level excitations and, therefore, that the microwa

ARTICLE4

R.G.Mani/PhysicaE

Rxx( )

0.00.00.00.04/5 Bf

B (T)

Fig.4.This gureshowsthedevelopmentoftheradiationinducedzero-resistancestateswiththeelectromagneticwavefrequency,f;overanintermediatef-range,whereazero-resistancestateoccursabout4Bf:NotethattheminimaareshiftedtoprogressivelyhigherBwithincreasingf:

isincreasedfrom9.79–15:6GHz;theRxx

decreasebelowthedarkRxxbecomesprogressivelyweaker,asapeakintheRxxdevelopswithincreasingf:AlthoughapluralityofoscillationsarenotevidentinRxxat15:6GHz;itisclearthat,at15:6GHz;BfcoincideswithneitheraminimumnoramaximuminRxx;asinthehigherfdatatobeexhibitedinFig.4.

Withafurtherincreaseinf;anumberofradiation-inducedoscillationsbecomeself-evidentinRxx;asshowninFig.4.Here,largeamplitudeoscillationsthatscalewithfoccurbelow0:3T;andtheseareattributedtotheradiation-inducedmagneto-resistanceeffect,whiletheweakresis-tanceoscillationsbetween0:3pBp0:4TareassociatedwiththeShubnikov–deHaaseffect.Thenoteworthyfeaturehereisthemanifestationofazero-resistancestateabout4Bf;whichshiftstoprogressivelyhigherB;withincreasingf:

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