Multiwall carbon nanotube Josephson junctions with niobium contacts [Elektronische Ressource] / vorgelegt von Emiliano Pallecchi
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Multiwall carbon nanotube Josephson junctions with niobium contacts [Elektronische Ressource] / vorgelegt von Emiliano Pallecchi

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Multiwall Carbon Nanotube JosephsonJunctions with Niobium Contacts�issertationzur Erlangung des Doktorgrades der Naturwissenschaften�Dr. rer. nat.)der naturwissenschaftlichen Fakult¨at II - Physikder Universit¨at Regensburgvorgelegt vonEmiliano Pallecchiaus FlorenzFebruar 2009Die Arbeit wurde von Prof. Dr. Ch. Strunk ange leitet.Das Promotionsgesuch wurde am � � � eingereicht.Das Kolloquium fand am 17.02.2009 statt.Pruf¨ ungsausschuss: Vorsitzender: Prof. Dr. Sergey Ganichev1. Gutachter: Prof. D r. Christoph Strunk2. Gutachter: Prof. Dr. Milena Grifoniweiterer Prufe¨ r: Prof. D r. Jascha Repp�lla mia famigliaContentsIntroduction �� Electronic Properties of Carbon Nanotubes 31.1 BandstructureofC arbonNanotubes . . .. . . . . . . . . ....... 31.1.1 Graphene. . . . . . . . . . . . ........ . . . . . . . . . 31.1.2 ZoneFolding. .. . . . . . . . . ........ . . . . . . . . . 41.1.3 RoleofDisorder . . . . . . . . . ........ . . . . . . . . . 61.2 TransportPropertiesofCarbonNanotubes . . . . . . . . . ....... 71.3 Coherenttransport . . . . . . . . . ........ . . . . . ....... 81.3.1 WeakLocalization . . . . . . . . ........ . . . . . . . . . 91.3.2 UniversalConduc tanceFluctuations. . .. . . . . . . . . . . . . 91.4 Coulombblockade . . . . . . . . . ........ . . . . . ....... 101.4.1 MasterEquation Description . . . . ... . . . . . . . . . . . 122 Proximity induced superconductivity �72.1 Superconductivity . . . . . . . . . ........ . . . . . ......

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Multiwall Carbon Nanotube Josephson
Junctions with Niobium Contacts
�issertation
zur Erlangung des Doktorgrades der Naturwissenschaften
�Dr. rer. nat.)
der naturwissenschaftlichen Fakult¨at II - Physik
der Universit¨at Regensburg
vorgelegt von
Emiliano Pallecchi
aus Florenz
Februar 2009Die Arbeit wurde von Prof. Dr. Ch. Strunk ange leitet.
Das Promotionsgesuch wurde am � � � eingereicht.
Das Kolloquium fand am 17.02.2009 statt.
Pruf¨ ungsausschuss: Vorsitzender: Prof. Dr. Sergey Ganichev
1. Gutachter: Prof. D r. Christoph Strunk
2. Gutachter: Prof. Dr. Milena Grifoni
weiterer Prufe¨ r: Prof. D r. Jascha Repp�lla mia famigliaContents
Introduction �
� Electronic Properties of Carbon Nanotubes 3
1.1 BandstructureofC arbonNanotubes . . .. . . . . . . . . ....... 3
1.1.1 Graphene. . . . . . . . . . . . ........ . . . . . . . . . 3
1.1.2 ZoneFolding. .. . . . . . . . . ........ . . . . . . . . . 4
1.1.3 RoleofDisorder . . . . . . . . . ........ . . . . . . . . . 6
1.2 TransportPropertiesofCarbonNanotubes . . . . . . . . . ....... 7
1.3 Coherenttransport . . . . . . . . . ........ . . . . . ....... 8
1.3.1 WeakLocalization . . . . . . . . ........ . . . . . . . . . 9
1.3.2 UniversalConduc tanceFluctuations. . .. . . . . . . . . . . . . 9
1.4 Coulombblockade . . . . . . . . . ........ . . . . . ....... 10
1.4.1 MasterEquation Description . . . . ... . . . . . . . . . . . 12
2 Proximity induced superconductivity �7
2.1 Superconductivity . . . . . . . . . ........ . . . . . ....... 17
2.2 MesoscopicJosephsonEffect . . . . . .... . . . . . . . ....... 18
2.3 Temperaturedependence . . . . . . ...... . . . . . . ....... 21
2.4 Theresistivelyandcapacitivelyshuntedmodel . . . . . . . . ..... .21
2.5 ExtendedRCSJmodel:effectoftheenvironmentandfinitetemperature 25
3 Experimental Details 3�
3.1 SampleLayout ... . . . . . . . ........ . . . . . ....... 31
3.2 SamplePreparation. . . . . . . . . ........ . . . . . ..... 3.1
3.3 MeasurementSetup . . . . . . . . . ........ . . . . . ..... 3.5
4 Supercurrent 39
4.1 Preliminarymeasurements . . . . . . ...... . . . . . . ....... 39
i4.2 SampleCharacterization . . . . . . . ... . . . . . . ....... 40
4.3 Superconductingrsoenance . . . . . .... . . . . . . ....... 42
4.4 Magneticfielddependence. . . . . . ...... . . . . . . ....... 51
4.5 MultipleAndreevreflections . . . . . .... . . . . . . ....... 54
4.6 SwitchingHistograms . . . . . . . . ........ . . . . . ..... 5.5
5 Coulomb Blockade 59
5.1 Coulombblockade . . . . . . . . . ........ . . . . . ....... 59
5.1.1 Stabilitydiagrams . . . . . . . . ........ . . . . . . . . . 63
5.1.2 Magneticfielddependence. . . . . ...... . . . . . . . . . . 65
6 Summary 7�
A Recipe 73
B filtering 75
Literature 77
iiIntroduction
Thetwocharacteristicfingerprintsofsuperconductivityaretheflowofdissipationless
supercurrentandperfectdiamagnetism. In1962J osephsonpredictedthatasupercur-
rentwouldalsoflowbetweentwosuperconductorsseparatedbyathininsulatingbarrier.
Thiseffectwasobserved in1963intunneljunctions. Afterthisfirstexperimentmany
differenttypesof“weaklinks”havebeenusedasabridgebetweentwosuperconducting
electrodes. Inmorerecentyearsproximityinducedsupercurrentthroughindividualcar-
bonnanotubeshasbeenobserved.Acarbonnanotubeisalargemoleculeformedbyone
ormoregraphenesheetsrolledupintoacylinder.Agreatvarietyofmesoscopicphenom-
enahasbeenstudiedincarbonnanotubesandtheobservationofsupercurrentthrough
thismoleculeopensthepossibilitytostudytheinterplaybetweenmesoscopicphysics
andsuperconductivity. Theexperimentalobservationofadissipationlesssupercurrent
ingatedcarbonnanotuberemainschallengingbecauseoftheextremesensitivityofthe
junctionstotheenvironmentandtonoisefluctuations. Insinglewallnanotubesasu-
percurrentismeasuredwhenabroaddegeneratelevelisinresonancewiththecontacts.
Theresultsarequalitativelyinagreementwiththetheoryrecentlydevelopedbyvan
HoutenandBeenakkerbu tthevaluesofthemeasuredcriticalcurrentsaremuchsmaller
thanwhattheorypredicts.Formultiwallcarbonnanotubesthesituationislessclear.In
molecularjunctionsthecriticalcurrentsaretypicallyseveralordersofmagnitudelower
thanwhatobservedinmoreconventionalJosephsonjunctionssothatthermalfluctua-
tionsarenotnegligibleevenatthelowesttemperaturereachedinexperiments.Ahigher
supercurrentwouldbedesirabletoallowamorethoroughstudyoftheproximityinduced
superconductivityinmolecularconductorsandfornewdevicessuchasthenanosquid.
Weaddresstheseissues bychoosingniobiumasasuperconductorandbydesigningan
optimizedonchipelectromagneticenvironment. Themaingoalofthisthesisisthe
investigationofdissipationlesssupercurrentinmultiwallcarbonnanotubesembedded
inacontrolledenvironment. Theenvironmentis meanttoreducethesuppressionof
thesupercurrentandallowstodisentangletheeffectsofthermalfluctuationsfromthe
12
intrinsicbehaviorofthejunction. Thisiscrucial fortheextractionofthevaluecritical
currentfromthemeasureddata.
Atpositivegatevoltage thecontactstransparencyisloweredandCoulombblockadeis
observed. Thisallowsto useCoulombblockadem easurementstofurthercharacterize
thenanotubeandtostudythephysicsofaquantumdotcoupledtosuperconducting
leads.Thelastpartofthisthesisisdedicatedtothemeasurementsofacarbonnanotube
JosephsonjunctionsintheCoulombblockaderegime.
Thethesisisorganizedasfollows: inthefirstchapterwebrieflyreviewthebasicelec-
tronicpropertiesofcarbonnanotubes. Firstwe introducethepeculiarbandstructure
thatnanotubesinheritfromgraphene,thenwediscusssomeofthemainrelevanteffects
observedintransportexperimentswithMWNTs . Inthesecondchapterweintroduce
theJosephsoneffectandwedescribetheextendedresistivelyandcapacitivelyshunted
junctionmodel(RCSJ).nIChapter3weillustrate thesamplepreparationandthemea-
surementschemesthatweused. InChapter4 wediscussthemeasurementsofour
Nb/MWNT/Nbjunction s. Firstwepresentacharacterizationofthejunctionandthen
wereportonthegatedependenceofthesupercurrent.FinallyweusetheextendedRCSJ
modeltoanalyzetheexperimentaldata.Chapter 5isdedicatedtomeasurementsinthe
Coulombblockade.Wefi rstpresentastudyofthedistributionofthepeakspacingand
thenwediscussthestabilitydiagrammeasuredinzeroandhighmagneticfield.Chapter1
ElectronicPropertiesofCarbon
Nanotubes
Inthefirstpartofthischapterweintroducethebandstructureofgrapheneandthen
derivethatofcarbonnanotubesbyimposingperiodicboundaryconditions. Inthesecond
partwewillbrieflyreviewthedifferenttransportregimestypicallyobservedinexperi-
ments.ThelastsectionisdedicatedtoCoulombblockade,thatwillalsobethefocusof
Chapter5wherethemeasurementsinthisregimearepresented.Thischap terismainly
basedonthebookofSaitoetal.[1]andonthereviewofRocheetal.[2]. Forthe
CoulombblockadesectionwefollowRef.[3,4]
1.1 BandstructureofCarbonNanotubes
1.1.1 Graphene
Grapheneisaplanarsheetformedbycarbonatomsarrangedinanhexagonallatticewith
2an sp hybridization.The 2s� 2p � 2p orbitalsformin-plane σ-bondsanddetermineth ex y
mechanical properties of graphene. The energiesassociated to the σ bands are far
awayfromtheFermienergy,thereforetheydonotusuallycontributetothetransport
properties.The p atomicorbitals,perpendiculartothegrapheneplane,donotoverlapz
withtheotherorbitalsandhybridizetoforma π(bondingandantibonding)delocalized
band. Thestructureofthe πbandofgraphenecanbecalculatedanalyticallyinthe
tight-bindingmodeland thenearestneighboursapproximation.
34 CHAPTER 1. ELECTRONIC PROPERT IES OF CARBON NAN OTUBES
Figure 1.1:The band structure of graphene. The valenceand the conductance
bands touch at the six corners of the first Bril louin zone.
Theresultingdispersion relationisgivenby:� � � �√ � � � �
3ka k a k ax y y2E(k�k ) =±t 1 + 4 cos cos + cos (1.1)x y
2 2 2
˚where tischosen-3.033eVtorperoducefirstprinciplescalculationsand a = 2.56Aisthe
latticeconstant.ThebandstructureisplottedinFig.1.1.Thevalenceandtheconduction
bandstouchatthesixcornersofthefirstBrillouin zone,thereforegraphene behaveslike
azerogapsemiconductor.
1.1.2 ZoneFolding
Asinglewallcarbonnanotube(SWNT)canbeobtainedbyrollingupagraphenesheet.
�Avectorconnectingtosites Aand A ofthegraphenelatticeiscalledchiralvector Ch
andcanbefullydefinedbyapair (n�m)suchthat
C = na + ma � (1.2)h � 2
witha anda thebasisvectorsofthelattice. Thegeometrical structureofacarbon� 2
nanotubecanberepresentedbytheindices (n�m)correspondingtothechiralvector
thatconnectstwopointsonthegraphenelatticethatcoincideoncethenanotubeis