Nonlocal resistivity in the fluctuation region of thin superconducting film.
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Nonlocalresistivityinthefluctuationregionofthinsuperconductingfilm.A.V.Nikulov,S.V.DubonosandY.I.KovalInstituteofMicroelectronicsTechnologyandHighPurityMaterials,RussianAcademyofSciences,142432Chernogolovka,MoscowDistrict,RussianFeder-ation.
AbstractThenonlocalresistivityinfluctuationregionofthinsuperconductingfilmsisobservedandinvestigated.Itissupposedthattheobservednon-localresistivityiscausedbyadifferenceofdistributionlawsofnormalandsuperconductingcurrentdensity.Themeasurementsshowthatthenonlocalresistivityissuppressedinlowmagneticfield.Theobtainedre-sultsareinterpretedastheabsenceofacoherenceinthefluctuationstatecalled”vortexliquid”.
74.60.GeInvestigationofthefluctuationphenomenaremainsoneofthemostpopularthemeofthesuperconductorphysics.Abignumberofworksconcerningthisthemehasappearedinlasttenyearsafterthediscoveryofhigh-temperaturesuperconductors,HTSC,butmanyimportantquestionsdonothavedefinitiveanswersforthepresent.NowitisobviousthatthetransitionintotheAbrikosovstatedoesnotoccurinthesecondcriticalfield,Hc2.ButitisnotclearwhatisthefluctuationstateexistingaboveandbelowHc2whichiscalledoftenas”vortexliquid”.Itisdifficulttoimaginethisfluctuationstatenow.Thewidespreadnaivenotionaboutthevortexliquidasaliquidofthevortexesgivesrisetodoubt.Thisnotionsupposesthatthevortexesexistinthevortexliquid.Consequentlyatransitionconnectedwithavortexdisappearancemustbeabovethevortexlatticemelting.Butnoexperimentevidenceofsuchtransitionhasbeenob-servedforthepresent.MoreovertheexperimentresultsabovevortexlatticemeltingaredescribedthesamefluctuationtheoreticaldependenceaboveandbelowHc2[1,2].Thereforethedenomination”vortexliquid”isnoquitegood.Thisdenominationsupposesthatthevortexisaparticle.Butthevortexisnotsomuchaparticleasasingularity.Thereforeitmaybethatthe”vortexlatticemelting”isnoadisappearanceofaorderinaparticledistributionbutadisappearanceamediuminwhichthesingularitiesexist.Nownotonlytheadequateimageofthevortexliquidisabsentbutalsoauniversallyrecognizedapproachtothedescriptionofthisstateisabsent.Agreatnumberofdifferenttheoreticalapproachesisconsequenceofalittlenumberofexperimentaldata.Thereforetheexperimentalinvestigationistimelythere.Oneofthemostimportantquestionisaquestionaboutcoherenceinthe”vortex
1liquid”.Thereforesomeinformationaboutthisfluctuationstatecanbeobtainedfrominvestigationofnonlocaleffects.Giavertransformer[3]maybeconsideredasoneofthemostknownexampleofnonlocaleffectsinsuperconductors.Measurementsofnonlocalresistivityforfluctuationinvestigationinbulkconventionalsuperconductorswasusedinworks[4].SimilarmeasurementsweremadeonbulkHTSCsamplesalso[5].Resultsof[4]showthatnosharpchangeoftheresistivityalongmagneticfieldisobservedatandabovethetransitionintotheAbrikosovstate(callednowas”vortexlatticemelting”).Thisresultmaybeinterpretedasabsenceofatransitionconnectedwithbreak-downoflongitudinalsymmetrypredictedinsomeworks(see[6]).Intheworks[4,5]thenonlocalresistivityalongmagneticfieldwasinves-tigated.Inthepresentworkweproduceresultsofinvestigationofnonlocalresistivityinzeromagneticfieldandacrossmagneticfield.WeusedamorphousNb1−xOxthinfilms.ThesefilmswereproducedbymagnetronsputteringofNbinanatmosphereofargonandoxygen.Thecrit-icaltemperatureTcofthesefilmsdependonoxygencontent.Inthisworkthefilmswithx≃0.2andTc1.86Kand2.46Kwereused.AmorphousNb1−xOxisatype-IIsuperconductorwithbigvalueoftheGinzburg-Landauparameterκandofthenormalresistivity,ρn:κ≃50,dHc2/dT=−22kOe/K,ρn=200mkOhmcm.Thetemperaturedependenceofnormalresistivityisveryweak,|dρn/dT|/ρn<0.0002K−1intheregion20-40K,wheresuperconductingfluctuationissmall.Theresistivityincreaseswithdecreasingtemperature.Thischangecanbeconnectedwithweaklocalization.Theusedfilmshaveveryweakpinning.Itwasshowninwork[2]thattheresistivedependenciesofthesefilmsaredescribedbyparaconductivitytheoryinawideregionbothaboveandbelowHc2.Theusedfilmstructureisshownschematicallyonfigure1.Thisstructurewasobtainedbyelectronlithographyandion-beametching.Thewidthofthecurrentcarrierstripisequalapproximately4mkm.Thebranchwidthisequalapproximately8mkm.Thedistancebetweenpotentialcontacts1-1isequalapproximately6mkm.Thedistancebetweenpotentialcontacts3and4is4mkm,between3and2is8mkm.Thewidthofthestripsofthepotentialcontactsis0.2mkm.Thefilmthicknessd=20nm.Thevoltagewasmeasuredwitharelativeerror0.0001.Thetemperaturewasmeasuredwitharelativeerror0.001.Amagneticfieldproducedbyasuperconductingsolenoidwasperpendiculartoafilmplane.Thetemperaturedependenciesoftherelationvii=Vii(T)/Vii,noncontacts1-1,4-4,2-2and3-3inzeromagneticfieldareshownonfigure1.WhereVii(T)isvoltageoncontacts1-1,4-4and2-2attemperatureTandVii,nisthesameatT=4.2Kwheresuperconductingfluctuationisverysmall.Therelationsvoltageonthecontactstothetransportcurrentvalue,I,inthenormalstateareV11,n/I=146Omh;V33,n/I=185Ohm;V44,n/I=111Ohm;V22,n/I=60Ohm.Thedependenciesvii(T)donotdependonthetransportcurrentvalueifIdoes