Kondo resonance enhanced supercurrent in single wall carbon nanotube Josephson junctions
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Kondo resonance enhanced supercurrent in single wall carbon nanotube Josephson junctions K Grove-Rasmussen ?and H Ingerslev J?rgensen and P E Lindelof Nano-Science Center,Niels Bohr Institute,University of Copenhagen,Denmark Abstract We have contacted single wall carbon nanotubes grown by chemical vapor deposition to super-conducting Ti/Al/Ti electrodes.The device,we here report on is in the Kondo regime exhibiting a four-fold shell structure,where a clear signature of the superconducting electrodes is observed below the critical temperature.Multiple Andreev re?ections are revealed by sub-gap structure and a narrow peak in the di?erential conductance around zero bias is seen depending on the shell ?lling.We interpret the peak as a proximity induced supercurrent and examine its interplay with Kondo resonances.
I.INTRODUCTION
Single wall carbon nanotubes(SWCNT)have been under intense investigation for more than a decade due to their unique mechanical and electrical properties.They are one-dimensional conductors with two conducting modes and when contacted to electrodes they behave as quantum dots,where phenomena as Fabry-Perot interference[1],Kondo e?ect[2] and Coulomb blockade[3,4]have been observed.The di?erent regimes can be accessed by indirectly controlling the coupling between the SWCNT and the contacts by choice of con-tact material.In the low transparency regime(closed quantum dot),electron transport is blocked except at charge degeneracy points,where electrons can tunnel through the SWCNT only one by one due to Coulomb blockade.When the transparency is increased(interme-diate regime)cotunneling of electrons becomes possible,which can give rise to the Kondo e?ect.Finally in the high transparency regime electrons on the SWCNT are not well de?ned and the phenomena observed(broad resonances)are due to interference of electron waves (Fabry-Perot interference).The possibility of contacting carbon nanotubes to superconduct-ing leads[5,6,7,8]opens up for the interesting study of e?ects related to superconductivity such as supercurrent and multiple Andreev re?ections[9]together with the above mentioned phenomena.In the Fabry-Perot regime recent experiments have con?rmed that the super-current is modulated by the quantized nature of the energy spectrum of the SWCNT,i.e., a Josephson?eld e?ect transistor with only two modes[10,11].Experimental access to the less transparent regimes[12,13,14,15]is even more interesting due to the possibility of probing the competition between e?ects related to Coulomb blockade and superconductivity. Coulomb blockade generally suppresses the supercurrent and interesting phenomena such as π-junction behavior has been observed in the closed quantum dot regime in nanowires[14]. For more transparent devices the supercurrent can be enhanced due to Kondo physics[16]. Both supercurrent and Kondo physics are two extensively studied manybody e?ects in con-densed matter physics and SWCNT Josephson junctions thus give a unique possibility to examine their interplay.The supercurrent is predicted to coexist with Kondo resonances provided that the Kondo related energy scale k B T K is bigger than the superconducting en-ergy gap?[16,17,18].The importance of the ratio between these parameters has recently been addressed in di?erent measurements[19].In this article we extend this investigation to SWCNTs contacted to superconducting leads in order to experimentally probe the interplay
between supercurrent and Kondo physics.We investigate the gate dependence of a narrow zero bias conductance peak interpreted as a proximity induced supercurrent and show that the observation of a supercurrent in Kondo resonances depends on the ratio between the two energy scales(k B T K/?)with a crossover close to1qualitatively consistent with theory.
II.EXPERIMENTAL DETAILS
SWCNTs are grown from catalyst islands consisting of Fe-oxide and Mo-oxide supported by aluminum nano-particles[20].Growth is performed by chemical vapor deposition at 850?C with a controlled?ow of gasses Ar:1L/min,H2:0.1L/min,CH4:0.5L/min.During heating the furnace is kept under an Ar and H2?ow,whereas cooling is done in Ar.We reduce cooling time by air-cooling the furnace.The substrate is a doped silicon wafer(used as back gate)with a500nm SiO2layer on top.Pairs of superconducting electrodes of Ti/Al/Ti (5/40/5nm)are de?ned directly on top of the SWCNT by electron beam lithography followed by optical lithography to de?ne the Cr/Au bonding pads.The?rst titanium layer of the metallic trilayer ensures good contact to the SWCNT,whereas the thicker middle aluminum layer is the actual superconductor in the device.Finally,the top layer of Ti is intended to stop oxidation of the aluminum.The gap between the source and drain electrode is typically around0.5μm.In the same evaporation process a four-probe device is made next to the S-SWCNT-S devices,which is used to measure the transition temperature T c= 760mK and the critical?eld around B c=100mT of the superconductor.From Bardeen-Cooper-Schrie?er(BCS)theory we deduce the superconducting energy gap?=1.75k B T c= 115μeV.The devices are cooled in a3He-4He dilution fridge with a base temperature around 30mK and we use standard lock-in techniques.
III.SUB-GAP STRUCTURE AND SUPERCURRENT
At room temperature the current through the device is gate dependent,which reveals that the SWCNT is semiconducting.Figure1(a)shows a bias spectroscopy plot at30mK of the SWCNT device in the Kondo regime.It is measured at negative gate voltages and thus transport takes place through the valence band,i.e.,tunneling of holes.The super-conductivity in the leads is suppressed by a relative weak magnetic?eld of180mT(>B c).
FIG.1:(a)Bias spectroscopy plot of a SWCNT device at30mK showing a four-fold Coulomb blockade shell structure.The numbers indicate the additional hole?lling,where big diamonds correspond to?lled shells.Four Kondo resonances K1-K4are identi?ed.A magnetic?eld of 180mT is applied to suppress superconductivity in the leads.(b)Bias spectroscopy plot for the same gate range as(a)but with the leads in the superconducting state.A sub-gap structure emerges,most clearly visible at±?/e and±2?/e(horizontal green dashed lines).The green dashed rectangles are the gate voltage regions shown in Fig.2(c)and2(d).
The plot shows Coulomb blockade diamonds[21]with a characteristic pattern of three small diamonds followed by a bigger diamond as indicated with white lines for hole?lling13-16. Such Coulomb blockade diamond structure indicates a four-fold degenerate shell structure due to spin and orbital degrees of freedom,where each shell contains two spin-degenerate orbitals[22].The?lled shells corresponding to the big Coulomb blockade diamonds are marked in Fig.1(a)by the additional number of holes on the SWCNT quantum dot.Due to intermediate transparency contacts signi?cant cotunneling is allowed which tends to smear the features.The charging energy and the level spacing between the shells are estimated
as half the source-drain height of the very faintly visible small diamonds and by the addi-
tional source-drain height of the big diamonds[23]giving U c～3meV and?E～4meV, respectively(see arrows Fig.1).A very rough estimate of the level broadeningΓ～1meV and the asymmetry in the coupling to source and drainα=Γs/Γd～0.4are extracted from the current plateaus at negative and positive bias(100nA and-60nA)at the white arrows.The current is modi?ed due to the four-fold degeneracy which enhances the in-tunneling rate with4compared to the out-tunneling rate giving(e/ˉh)4ΓsΓd/(4Γs+Γd)and (e/ˉh)(4ΓdΓs/(Γs+4Γd)for negative and positive bias polarity,respectively[24].Further-more,four Kondo resonances K1-K4are identi?ed(green arrows)and labeled in ascending order based on their Kondo temperatures.The Kondo temperatures are estimated by?tting the normal state conductance versus V sd(solid line in Fig.3a-b)to a Lorentzian line shape. The half width at half maximum of each Lorentzian?t yields the estimated Kondo temper-ature giving T K～2K,4.5K,5K and6K for K1-K4.For hole?lling13-15,conductance ridges at low?nite bias are seen instead of zero bias Kondo resonances.The exact origin of these features are not fully understood,but they are attributed to inelastic cotunneling through two slightly split orbitals in the shell,which might include Kondo physics as well [25].We note that these lines are not related to superconductivity.
Figure1(b)shows a bias spectroscopy plot at low bias voltages for the same gate range as Fig.1(a)with the leads in the superconducting state.A sub-gap structure clearly appears [9].The peaks in di?erential conductance at V sd=±2?/e～±230μV are attributed to the onset of quasi-particle tunneling.At lower bias the transport is governed by Andreev re?ections,which are possible due to the intermediate transparency between the SWCNT and the superconducting leads[26].Features at biases V n=±2?/(en),n=2,3,...are expected due to the opening of higher order multiple Andreev re?ection processes as the bias is lowered[27,28].Peaks at V sd=±?/e～±115μV are clearly seen consistent with the energy gap found from BCS theory.Furthermore,for some ranges in gate voltage a narrow zero bias conductance peak is seen.We note,that this zero bias peak is visible in most of the Kondo resonances and is the subject to analysis below.
These above mentioned e?ects due to superconductivity are more clearly revealed in high resolution data shown in Fig.2(c)and2(d)corresponding to the green dashed rectangles in Fig.1(b).Figure2(a)and2(b)show the same gate and bias regions as(c)and(d) with the leads in the normal state for comparison.Clearly the sub-gap structure is due to the proximity of the superconducting leads.The peaks at±2?/e and±?/e are mostly
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-0.2dI/dV [e 2
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V s d [m V ]FIG.2:(a-b)Bias spectroscopy plot at 30mK with the leads in the normal state (B =180mT)for Kondo resonance K4and K1,respectively.(c-d)High resolution data with the leads supercon-ducting for the same gate and bias voltages as in the normal state above.The corresponding gate regions are shown by the dashed green rectangles in Fig.1(b).A sub-gap structure appears at bias voltage ±2?/e and ±?/e indicated by the green dashed lines.This is particular clear in the Coulomb blockade region (d)and also seen in the green traces,which are dI/dV versus bias curves extracted from the plots.A zero bias conductance peak (red arrow)is also visible throughout Kondo resonance K4as shown by the red trace in (d)and for some gate voltages in (c).
pronounced in the Coulomb blockade region as expected due to lower e?ective transparency
[27](d)while being more smeared in the high conducting region of K4(c).Green curves show bias cuts,where higher order multiple Andreev re?ection features are faintly visible in (c).A strong gate dependence of the sub-gap structure is observed when the gate voltage is tuned closer to the Coulomb resonances on each side of K1from the Coulomb diamond with even occupation.This behavior has previously been observed [9]and explained by the interplay between multiple Andreev re?ection and a resonant level [29,30].The zero bias conductance peak indicated by the red arrow is clearly visible in Kondo resonance K4(red trace in (c))and also present for some gate voltages in (d).Similar behavior of a zero bias peak in Kondo
resonances have been observed in other devices[13].We interpret the zero bias conductance peak as being due to a proximity induced supercurrent running through the SWCNT.The magnitude of the supercurrent is estimated by the area of the peak giving a typical value in the order of I m～0.2nA.A similar analysis of a zero bias conductance peak as supercurrent has successfully been carried out for an open quantum dot[11],i.e.,without Coulomb blockade e?ects.We note that an alternative interpretation of the origin of the zero bias peak based on quasiparticle current(multiple Andreev re?ections)with a cut-o?for higher order multiple Andreev re?ection processes has also been suggested[31],but in this article the supercurrent interpretation will be pursued.The value of the measured supercurrent is highly suppressed compared to its theoretically expected value for one spin-degenerate level with the deduced asymmetric coupling(α=0.4)at resonance I res0=2e?/ˉh(Γmin/Γ)～8nA in the broad resonance(short)regimeΓ>?,whereΓmin=min(Γs,Γd)～0.3meV[32]. Despite having two spin-degenerate levels in the SWCNT,only one level is available due to Coulomb blockade.
The suppression is partly explained within an extended resistively and capacitively shunted junction model due to interaction of the SWCNT Josephson junction with its elec-trical environment.The electrical environment for this device is the low(serial)resistance between the Josephson junction and the bonding pads as well as the capacitance between the source and drain bonding pads via the backgate.The low serial resistance turns out to play a crucial role making the device an underdamped Josephson junction[10,11,33,34]. This means that the full value of the critical current is never measured due to thermally activated phase-slips.A more intuitive understanding is obtained by the mechanical analog to the Josephson junction of a?ctious particle in a tilted washboard potential,where the tilt is given by the current and the phase di?erence between the superconductors is”running”as the?ctious particle moves in the potential.When the particle stays in a minimum of the washboard potential(constant phase),a supercurrent is seen.However,as the current increases the washboard potential is tilted and at the critical current the particle can slide into the next minimum.If thermal excitations are signi?cant this process happens at lower current than the critical current.Since the junction is underdamped,the friction of the par-ticle is low and it thus easily acquires a”run away”phase,that suppresses the supercurrent, which results in a much lower measured supercurrent.In contrast to the reported under-damped carbon nanotube Josephson junction in the Fabry-Perot regime[11],the e?ect of
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d I /d V [
e 2/h ]V sd
[mV]
d I /d V [
e 2
/h ]
d I /d V [
e 2/h ]
V sd [mV]FIG.3:dI/dV versus V sd for Kondo resonances K1-K4shown in Fig.1(a)illustrating the e?ect of superconducting leads.(a-b)Solid lines and circles are with the leads in the normal and supercon-ducting state,respectively.(c)The four Kondo resonances K1-K4for small bias voltages with the leads in the superconducting state.The measured supercurrent given by the zero bias peak area is zero for the lowest value of the ratio k B T K /?,while it increases as this ratio is increased.
Coulomb blockade and single hole tunneling also contribute to the suppression of the super-current,because Cooper pair transport is a two particle tunneling process.A quantitative analysis of the suppression due to Coulomb blockade is outside the scope of this article.This issue is being addressed in a separate work,where the on-chip electrical circuit of the SWCNT Josephson junction has been modi?ed and the e?ects of Coulomb blockade thus can be compared to theoretical calculations [35].Finally,we note that noise e?ects giving rise to thermally activated phase slips can be analyzed in the overdamped case [36].
IV.KONDO PHYSICS AND SUPERCURRENT
We now return to the Kondo resonances K1-K4and analyze the interplay between Kondo
physics and supercurrent.The solid curves in Fig.3(a)and 3(b)show bias cuts with the leads in the normal state through the center of Kondo resonance K2and K4,respectively (see Fig.1(a)).The circles correspond to the behavior when the leads are superconducting.In both cases an enhancement of the di?erential conductance is observed for bias voltages between
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00 I m
[n A ]k B T K / G N
[e 2/h ]V gate
[V]
I m [n A ]FIG.4:(a)The measured supercurrent is zero for K1and shown to increase as a function of k B T K /?(K1-K4).An exponential ?t to the data points is given by the solid curve as guideline,where the Kondo temperature is based on the width of the resonance (black diamonds).The red squares are the Kondo temperature obtained from the temperature dependence (K1,K3and K4).(b)Measured supercurrent versus gate voltage in the range with the Kondo resonances K1-K4,where the additional hole number is given for ?lled shells as in Fig.1(a).A ?nite supercurrent is seen in the center of the broader Kondo resonance K2,while being zero in the center of narrowest Kondo resonance K1.This behavior does not re?ect the normal state conductance G N shown for the same gate range below in (c).
±2?/e and a zero bias conductance peak is present due to supercurrent.The measured supercurrent is largest for the Kondo resonance with the highest Kondo temperature (K4),i.e.,broadest Kondo resonance.In Fig.3(c)bias sweeps at the center of all four Kondo resonances are shown with the leads in the superconducting state.The Kondo temperature normalized by the superconducting energy gap (k B T K /?)is the important parameter and is given for each resonance in the ?gure.It is seen that the measured supercurrent vanishes for the lowest ratio (blue circles)while it emerges and increases as the ratio is increased.The crossover is close to k B T K /?～1.
To illustrate this point more clearly,the measured supercurrent versus k B T K /?is plotted
in Fig.4(a)for the four Kondo resonances analyzed above (black diamonds).The solid curve shows a guideline to the eye based on an exponential ?t to the available data points.The overall trend is qualitative consistent with existing theory,which predicts a suppression of
the supercurrent in the socalled weak coupling regime(k B T K??),while the supercurrent coexists with Kondo resonances in the strong coupling regime(k B T K??)[17,18].The red squares show the measured supercurrent where the Kondo temperature is extracted from the temperature dependence for completeness(only data available for K1,K3and K4)[37].
Finally,Fig.4(b)shows the measured supercurrent as a function of gate voltage in the range including the four Kondo resonances.It is strongly gate dependent illustrating e?ects of the four Kondo resonances.Figure4(c)shows the zero bias conductance G N with the leads in the normal state for the same gate range.The supercurrent does not directly re?ect the normal state conductance G N as in the case of an open quantum dot[10,11],where the supercurrent is uniquely determined by the normal state conductance.This is most clearly seen by comparing Kondo resonance K1and K2.No supercurrent is present in the center of the Kondo resonance K1despite the high normal state conductance,while a?nite supercurrent is present in Kondo resonance K2with equally high normal state conductance in contrast to the behavior expected in the open quantum dot regime.Similarly,the Kondo resonances K3and K4have almost the same normal state conductances,but very di?erent measured supercurrent.These observations support the above analysis that the interplay between Kondo physics and superconductivity has the fraction k B T K/?as the important parameter for the observation of supercurrent in Kondo resonances,i.e.,the bias width of the Kondo resonances and not only their normal state conductance is important.We also note that the measured supercurrent in diamond4,8and12is zero due to Coulomb blockade. The supercurrent in the high T K Kondo resonances can thus be view as being enhanced from the suppressed values by Coulomb blockade and the single spin due to the formation of Kondo resonances.Furthermore,the overall behavior of the supercurrent of these four Kondo resonances also indirectly indicates aπto0transition of the current phase relation of the Josephson junction as a function of the parameter k B T K/?[17,18].Similar gate voltage behavior has been observed in Ref.[15],but the authors do not show the magnitude of the supercurrent as a function of Kondo temperature.We end by noting that for large Kondo temperatures compared to the superconducting energy gap(K4),the observed gate voltage dependence of the supercurrent resembles the behavior of a superconducting single electron transistor,i.e.,the supercurrent obtains a sharp maximum at the gate voltage corresponding to the center of the odd diamond[38].
V.CONCLUSION
In conclusion SWCNTs have been contacted to superconducting Ti/Al/Ti leads creating SWCNT Josephson junctions.We observe sub-gap structure due to multiple Andreev re-?ections and a narrow zero bias conductance peak.The zero bias peak is interpreted as a proximity induced supercurrent with a suppressed magnitude due to the underdamped na-ture of the Josephson junction and Coulomb blockade.We examine its interplay with Kondo resonances and the measured supercurrent is shown to coexist with Kondo resonances which have high Kondo temperatures compared to the superconducting energy gap,while being suppressed when the Kondo temperatures becomes comparable with the superconducting energy gap,qualitative consistent with existing theory.
Acknowledgement
We like to thank Karsten Flensberg,Tom′aˇs Novotn′y and Jens Paaske for fruitful discus-sions.Furthermore,we wish to acknowledge the support of the Danish Technical Research Council(The Nanomagnetism framework program),EU-STREP Ultra-1D and CARDEQ programs.
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