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2 1 0 2 Scanning microscopiesof superconductors atvery lowtemperatures n a V. Crespo, A. Maldonado, J.A. Galvis, P. Kulkarni,a I. Guillamon,a,b J J.G.Rodrigo,H. Suderow, S. Vieira,a,1 S. Banerjee,c P. Rodiered 9 a Laboratorio deBajas Temperaturas, Departamento deF´ısica delaMateriaCondensada, InstitutodeCienciadeMateriales ] Nicolás Cabrera, Universidad Autońoma de Madrid, E-28049 Madrid, Spain n bH.H.WillsPhysicsLaboratory, Universityof Bristol, TyndallAvenue, BristolBS8 1TL, UK o cDepartment of Physics, Indian Institute of Technology, Kanpur 208016, U.P., India c dInstitut Neel, CNRS/UJF, 25 Avenue desMartyrs, B.P. 166, 38042 Grenoble Cedex 9, France - r p u s . t a Abstract m We discuss basics of scanning tunneling microscopy and spectroscopy (STM/S) of the superconducting state with - d normalandsuperconductingtips.WepresentanewmethodtomeasurethelocalvariationsintheAndreevreflection n amplitude between a superconducting tip and the sample. This method is termed Scanning Andreev Reflection o Spectroscopy(SAS).WealsobrieflydiscussvorteximagingwithSTM/Sunderanappliedcurrentthroughthesample, c and showthevortexlattice as afunction of theangle between themagnetic fieldand sample’s surface. [ 1 Keywords: Scanning TunnelingMicroscopy andSpectroscopy, Vortex lattice, dichalcogenides. v 8 6 8 1. Introduction ple,vortexlatticeelasticitystudiestreatvorticesas 1 . ropeswitharigidcenterin3Dorasdisksin2D,and 1 Using Scanning Tunneling MicroscopyandSpec- are important in explaining vortex lattice disorder 0 2 troscopy (STM/S), one can, in principle, image and melting [6–9]. In anisotropic superconductors, 1 many features of superconductors. In particular, non-local physics leads to anomalous vortex lattice : thepositionofvorticesandthesymmetryofthelat- symmetries[10,11].Magnetism may increase vortex v i tice, as well as the spectroscopy inside and around density or change its symmetry[12,13]. Conduc- X vortexcores[1,2].Avortexconsistsofsupercurrents tance or Tc oscillations, observed in regular arrays r surrounding a magnetic core, and the Cooper pair of dots or other nanostructures, highlight vortex a wavefunctionslips its phase by 2π in a ring around pinning in terms of force balance[14]. The observa- itscenter[3–5].Thequantizedfinitecirculationim- tion of peaks in the density of states in the center pliesthatthesupercurrentvelocityhastodivergeat of the vortex cores is understood in terms of the the center ofthe vortex.This divergenceis avoided smooth changes of the Cooper pair wavefunction astheCooperpairwavefunctiondropscontinuously whenapproachingthe centerofthe vortex[15–18]. towardsthe centerandbecomeszeroexactlyatthe Inthispaperwereviewsomeaspectsoftunneling vortex core.Materials Science and nanostructuring spectroscopy relevant for the study of supercon- havebeenusedtohighlightdifferentaspectsofvor- ductors, and discuss recent developments enabling tices,givingnewphysicsorapplications.Forexam- new imaging possibilities, such as Scanning An- dreev Reflection Spectroscopy. Measurements have 1 *Correspondingauthor: [email protected] been taken in several dilution and 3He refrigerator Preprintsubmitted toElsevier 10January 2012 STM/Sset-upsdescribedelsewhere[2,19,20]. fields.ThetunnelingcurrentI betweentipandsam- ple can be written as I(V) ∝ R dE[f(E − eV) − 5 f(E)]NT(E−eV)NS(E),andistheresultofthecon- 34 E) (arb. units)5 (a) pWvolelhuNetniSo,nthwoeefitgthihpetedidsenbmsyitatideheseooFffesrtamatnieofsunonfcsttuiipponeNrfcTo(anEnd)du[1cs,ta2imn1]g-. N(S 2 0.0 0.5 1.0 1.5 2.0 metal, NT is energy-independent, and the differen- Energy (meV) tial tunneling conductance σ = dI/dV is simply s) 1 NS(E) smearedby the Fermi function[1,22]. When t ni 200 kBT islowenough,σ ispracticallyequaltoNS(E), nce (arb. u 1105 N(E) (arb. units)T150 I (arb. units)120000 biasni)ugg,tnacinwofidnchademnunteclatiynasucninrrcefleeamumseiennanycgtebustehntecsheiegtrnetfiaminfiinapctlaeyrndactetlo-yucmorseinmn,vgeotahlfrureeotdmitou(nFnn[on2igi3es.l]1e-. a 5 0.00 0.05 0.10 0.5 1.0 Considernow,forexample,atipwithaδfunction ct Energy (meV) Bias voltage (mV) likesharppeakattheFermilevel,inanotherwisefi- u d 0 nite andenergyindependentdensity ofstates,such n (b) o astheoneproducedbyalocalizedstateclosetothe c -5 g 0.5 1.0 1.5 tip[24,25]. In that case, the I(V) curve directly re- n Bias voltage (mV) i flectsthedensityofstatesofthesample,withapeak l l nne 15 (c) atthegapedge.Theconductanceσhascorrespond- u ingly pronounced maxima and minima, and passes T through zero exactly at the position of the peak in 10 I(V).Whenincreasingtemperature,thecurrentbe- low the gap edge increases exponentially, reflecting 5 the thermal behavior of the tail of the Fermi function[26],butfeaturesinσatthegapedgearelargely unaffected(Fig.1b).Ifthedensityofstatesofthetip 0 1.0 1.5 2.0 2.5 3.0 iswellknownandindependentoftemperature,then Bias voltage (mV) thede-convolultionofthesample’sdensityofstates from the I-V curve or from the tunneling conduc- Fig.1.a)Calculated tunneling conductance between anor- tanceremainsprecisewhenincreasingtemperature. mal tip and a s-wave BCS superconductor as a function Localizedstatefeatureswhichgivepeakshapedden- of the bias voltage at Tc/65 (blue line) and at Tc/2 (red sities of states have been observed in some cases line). We use NS(E) as shown in the inset (with peak at closetodefectsorimpurities[24,25,27,28].Tipswith ∆=1.76kBTc=1meV).b)Tunnelingconductancebetweena tiphavingaGaussianshapedpeakofthedensityofstatesat impurities locatedclosetothe apexcouldtherefore theFermilevel,withawidthof15µeV (NT(E)asshownin give interesting results, although they still need to theleftinset)andasuperconducting samplewiththesame be realizedin acontrolledway. density of states NS(E) as in a, at Tc/65 and at Tc/2. In- Asuperconductingtipleadstoevenbetterresults. set shows the corresponding I(V) curves. c) Tunneling con- The form and properties of the density of states of ductance between tip and sample with the same density of statesasina)atTc/65andatTc/2.Biasvoltagelabelsfor tipsmadeofwellknownsuperconductorshavebeen caregiveninmVatthebottom, andforaandbinmVat previouslyreportedwithdetail[2,29–37].Thequasi- the top. particlepeakslocatedatthegapedgeleadtoasharp anomaly at the sum of the tip and sample’s super- conductinggaps(Fig.1c).Whenincreasingtemper- 2. Spectroscopy withsuperconducting tips ature,thewidthofthecorrespondinganomalydoes notchange,makingthedeterminationoftheLDOS One objective of a tunneling spectroscopy imag- ofthesamplethroughde-convolutionaccurateatall ingexperimentinasuperconductoristoobtainwith temperatures [38,39]. highestprecisiontheenergydependenceoftheden- sityofstatesofthesuperconductorNS(E)asafunc- tionofthepositionatalltemperaturesormagnetic 2 Normalized Conductance (G/G)N001...050 GN = 0.2 G0 Normalized Conductance (G/G)N001...050 GN = 0.006 G0 liTnlenoovhwteefeulrbs[et3teu0eirt,sn4ee,0mye,elx4potp1ecal]rao,anlrtoaeuptndrhhdeeausrsn,tethitmielhsyepennoosccrwiouttau.irvnrlIdeetnneftepexnaapdarteuubtrierlcieemutlowedanerhtts,ishicag[eh2tnr,im4htn2haga]es,l. (a) 0.5 1.0 0.5 1.0 excitations at voltages below the superconducting Voltage (mV) Voltage (mV) gap is exponentially small. Andreev reflection between tip and sample is always present, and the corresponding current depends exponentially on the tunneling barrier[43]. Therefore, reducing the tunnel barrier at the lowest temperatures leads to the observation of a small current at bias voltages belowthesuperconductinggapwhichexponentially (b) grows when the distance between tip and sample is reduced[44]. For instance, using a superconducting tip and a normal sample, with a tunneling conductance of around some tens of µS (i.e. some 0.1 G0, where G0 is the quantum of conductance), the Andreev reflectionaccountsforthe observation of a tunneling conductance of some per cent the high voltage conductance. When scanning with a (c) superconductingtipasuperconductingsample,An- dreevreflectionisfurthersuppressed,astheprocess Fig.2.ScanningAndreevSpectroscopy ofthevortexlattice requires bouncing back and forth four electronic of NbSe2 usingatipof Pbat0.3K.In leftpanels weshow states, instead of the two states involved in a N-S experiments on the vortex lattice with a short tip-sample Andreev reflectionprocess[45]. distance(conductanceat4mVisof17µS,Andreevreflection Thus, scanning with, e.g. a superconducting tip is observed), and in the right panels we show experiments of Pb, on a sample with superconducting and nor- made using a larger tip-sample distance (conductance at 4 mV is of 0.5µS, Andreev reflection is suppressed due to malareas,leadstoaconductanceatafinitevoltage the high tunneling barrier). In a) we show the tunneling below the superconducting gap which changes as a conductance at a vortex core (red points), and in between functionoftheposition,beingsignificantlylargeron vortices(bluepoints).Higherconductanceatthevortexcores top of the normal areas. Of course, the experiment is due to Andreev reflection between the superconducting needstobemadeatlowenoughtemperaturestoen- tip and the NbSe2 sample, only visible when tip-sample distance is short enough (here at 17µS). Violet and green surethattheresultdoesnotcomefromthermalex- lines show the voltages at which the spectroscopic images citations.Moreover,localvariationsinthemagnetic inbanccarebuiltof.Theimages builtwiththetunneling field may result in changes in the tip’s density of conductanceat0.5mV(showninbinvioletframes),clearly stateswhichinducepairbreakingeffects,producing show the vortex lattice if the tip-sample distance is short similarlyahigherlowbiasconductance[31].Chang- (left panel, 17µS) due to Andreev reflection between the superconductingtipandthenormalvortexcore.Theimage ingthetip-sampledistanceisthemosteffectiveway built with the tunneling conductance at the same voltage toseparateAndreevprocessesfromothervariations is featureless when the tunneling conductance is low (right ofthelowbiasvoltageconductanceasafunctionof panel,0.5µS).Colorcodeisshownasabaratthecenterusing theposition.InFig.2weshowresultstakenatacon- the same scale as in the y axis of a, namely the tunneling ductanceof17µS(leftpanelsofFig.2),andcompare conductance normalized to the value at high voltages. In c we show the images constructed from the data at 1 meV, them with results takenat a conductance of 0.5µS using the color code from the bar at the center. Observed (right panels of Fig.2), which is around 0.39% G0. features (star shaped vortex core) do not depend on the While thermal excitations or pair breaking depend tip-sample distance, and have been discussed in previous ontheactualdensityofstatesofthetipandshould publications[2,29–36]. bepresentatalltunnelingtip-sampledistances,An- 3. Scanning Andreev Reflection dreev reflections will decrease exponentially with Spectroscopy withsuperconducting tips. distance. The left panel of Fig.2b shows the vortex latticeofNbSe2at0.1Tviewedbyplottingasafunc- Superconducting tips also allow, on the other tionofthepositionthevalueoftheAndreevconduc- hand, to probe the Josephson effect at the local 3 tance.Thesignatureofvorticesiswashedoutwhen applied current. Several STM/S experiments have imagesaretakenatlowtunneling conductance,be- been designed for topography measurements under lowµS,asshownintherightpanelofFig.2b.When an applied current. The arrangement requires to theimageisbuiltfromthevalueoftheconductance ground one side of the sample and apply a bias to at1mVtheobservedfeaturesareduetochangesin theotherside,withacurrentfixedbytheresistance the localdensity ofstates,andhavebeen discussed ofthesampleandthebiasvoltage[20,46].Inorderto previously[2,29–36].Namely,thedensityofstatesat study a superconductor, one requires knowledge of thecenterofthevortexcoreishighandleadstohigh thefullNS(E)dependence.Recently,wehavedevel- conductanceat1mVwhenusingasuperconducting oped new STM/Scircuitry andmethods to be able tipofPb,andthecharacteristicstar-shapefoundin tomakeI-Vmeasurementsasafunctionoftheposi- NbSe2 is observed in-between vortices. This obser- tionandthe currentusingnormaltips[20].InFig.3 vation is independent of the value of the tunneling weshowavortexlatticeimageofNbSe2obtainedby conductance,as isshowninFig.2c. measuringateachpositionafullI-Vcurve,andap- This demonstrates that the localized electronic plyingacurrentof10mAthroughthesample,at4.2 statesinside the vortexcorescancarryanAndreev K.Correspondingcurrentdensityisof0.4104A/m2. current, which peaks at the vortex core. Note that Current flow can be expected to be homogeneous, Andreev reflection between a conventional s-wave because the London penetration depth λ is much superconductorandametalwithfullspinpolariza- largerthanthecoherencelengthξ[18].Hereweplot tion is not allowed. Thus, Scanning Andreev Spec- the normalizedzerovoltageconductance as a func- troscopy can be developed in future as an effective tion of the position[2]. The vortex lattice is clearly toolto study localspin polarizationof materialsat viewed, so that the current is below the de-pinning verylowtemperatures. value.Weimagethereforethepinnedvortexlattice. Further measurements at lower temperatures, and 4. Current drive scanning tunneling as a function of the current and the magnetic field microscopyand spectroscopy. areunder way. 5. Scanning tunneling microscopy and spectroscopy inavector magneticfield. 60(cid:176) 70(cid:176) 76(cid:176) Fig. 3. The pinned vortex lattice of NbSe2 observed using conventionalscanningtunnelingspectroscopywithanormal tip under an applied current of 10 mA at a magnetic field of 0.5 T and at 4.2 K. To obtain the image, full I-V curves Fig. 4. Vortex lattice of NbSe2 as a function of the angle are taken at each position. The conductance at zero bias is of the applied magnetic field with respect to the surface. plotted as a function of the position. At this temperature Images are taken at 0.5 T and 1.2K. Top panels show the (4.2K),thedependenceoftheI-Vcurveswithinvortexcores real space images, and bottom panels their Fourier trans- andinbetween vorticesasafunctionoftheappliedcurrent forms. Red lines and points highlight the Bragg peaks of ismixedwith the temperature smearing. the vortex lattice. When increasing the angle, the hexagon elongates,andleavespracticallyastripelikearrangementat Itisalsoimportanttoimagevaryingrelevantther- 76o.GreylinesandpointsshowthepositionofBraggpeaks modynamic and transport parameters, such as an withsmalleramplitude. 4 Thecontroloverthedirectionofthemagneticfield Acknowledgements is another important aspect which allows studying highly anisotropic samples. In particular, the vor- WespeciallyacknowledgesupportfromNESpro- texlatticeinlayeredcompoundsisexpectedtoshow gram.ThisworkwasalsosupportedbytheSpanish many peculiarfeatures relatedto the modifications MEC (Consolider Ingenio Molecular Nanoscience of intervortex potential when the magnetic field is CSD2007-00010 and FIS2008-00454 and ACI2009- turned from being perpendicular to the layers[47– 0905 programs) and by the Comunidad de Madrid 49]. Recently, we have developed a dilution refrig- throughprogramNanobiomagnet.TheLaboratorio eratorthree-axisvectormagnetSTM/Sset-up,and de Bajas Temperaturas is associated to the ICMM couldmeasuretheangulardependenceofthevortex ofthe CSIC. lattice in NbSe2. The density of vortices decreases when the z-axis component of the magnetic field drops,followingcos(θ−θm),withθmbeingthemis- References alignmentofthenormaltothesurfaceofthesample withrespecttothezcomponentofthemagneticfield [1] O. Fischer, M. Kugler, I. Maggio-Aprile, C. 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