A superconductor-normal metal-superconductor mesoscopic Josephson junction
has been realized in which the critical current is tuned through normal current
injection using a symmetric electron cooler directly connected to the weak
link. Both enhancement of the critical current by more than a factor of two,
and supercurrent suppression have been achieved by varying the cooler bias.
Furthermore, this transistor-like device demonstrates large current gain
$\sim$20) and low power dissipation

A. Anthore

A. M. Savin

Andreev A. F.

F. Giazotto

J. P. Pekola

J. T. Flyktman

Applied Physics Letters

English

arXiv

Crossref

Cold electron Josephson transistor

A superconductor-normal metal-superconductor mesoscopic Josephson junction has been realized in which the critical current is tuned through normal current injection using a symmetric electron cooler directly connected to the weak link. Both enhancement of the critical current by more than a factor of two, and supercurrent suppression have been achieved by varying the cooler bias. Furthermore, this transistor-like device demonstrates large current gain (∼20) and low power dissipation.Peer reviewe

Savin, A. M.

Pekola, Jukka P.

Flyktman, J. T.

Anthore, A.

Giazotto, F.

Aaltodoc Publication Archive

This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Savin, A. M. & Pekola, Jukka & Flyktman, J. T. & Anthore, A. &Giazotto, F.Title: Cold electron Josephson transistorYear: 2004Version: Final published versionPlease cite the original version:Savin, A. M. & Pekola, Jukka & Flyktman, J. T. & Anthore, A. & Giazotto, F. 2004. Coldelectron Josephson transistor. Applied Physics Letters. Volume 84, Issue 21. P.4179-4181. ISSN 0003-6951 (printed). DOI: 10.1063/1.1756192.Rights: © 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other userequires prior permission of the author and the American Institute of Physics. The following article appearedin Applied Physics Letters and may be found athttp://scitation.aip.org/content/aip/journal/apl/84/21/10.1063/1.1756192All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)Cold electron Josephson transistorA. M. Savin, J. P. Pekola, J. T. Flyktman, A. Anthore, and F. Giazotto  Citation: Applied Physics Letters 84, 4179 (2004); doi: 10.1063/1.1756192 View online: http://dx.doi.org/10.1063/1.1756192 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/84/21?ver=pdfcov Published by the AIP Publishing  Articles you may be interested in Parallel array of YBa2Cu3O7−δ superconducting Josephson vortex-flow transistors with high current gains Appl. Phys. Lett. 103, 092601 (2013); 10.1063/1.4819461  Charge sensitivity of the inductive single-electron transistor Appl. Phys. Lett. 87, 092502 (2005); 10.1063/1.2034096  Charge and spin effects in mesoscopic Josephson junctions (Review) Low Temp. Phys. 30, 554 (2004); 10.1063/1.1789291  Control of Coulomb blockade in a mesoscopic Josephson junction using single electron tunneling J. Appl. Phys. 95, 8059 (2004); 10.1063/1.1751231  Radio-frequency-induced transport of Cooper pairs in superconducting single electron transistors in a dissipativeenvironment J. Appl. Phys. 95, 6325 (2004); 10.1063/1.1713024    This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Wed, 20 May 2015 03:48:10Cold electron Josephson transistorA. M. Savin,a) J. P. Pekola, J. T. Flyktman, and A. AnthoreLow Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, FinlandF. GiazottoNEST-INFM and Scuola Normale Superiore, I-56126 Pisa, Italy~Received 20 February 2004; accepted 7 April 2004; published online 6 May 2004!A superconductor-normal metal-superconductor mesoscopic Josephson junction has been realized inwhich the critical current is tuned through normal current injection using a symmetric electroncooler directly connected to the weak link. Both enhancement of the critical current by more thana factor of two, and supercurrent suppression have been achieved by varying the cooler bias.Furthermore, this transistor-like device demonstrates large current gain ~;20! and low powerdissipation. © 2004 American Institute of Physics. @DOI: 10.1063/1.1756192#Transport dynamics in mesoscopic structures where nor-mal metals ~N! are coupled with superconductors ~S! arecurrently the focus of extensive research.1,2 This stemsmainly from the relevance these systems have both from thefundamental physics point of view and in light of their pos-sible exploitation in nanoelectronics. In diffusive SNS junc-tions, where the length of the N region exceeds the elasticmean free path, coherent sequential Andreev scattering3 be-tween the superconductors may lead to a continuum spec-trum of resonant levels1 responsible for carrying the super-current flow through the structure. The Josephson current isgiven by supercurrent spectrum weighted by the occupationnumber of correlated electron-hole pairs that is determinedby the quasiparticle energy distribution in the N region of thejunction. By changing the latter through current injectionfrom additional nonsuperconducting terminals connected tothe N region4 both supercurrent suppression5 as well as itssign reversal ~p-transition! were demonstrated.6 As predictedin Refs. 7 and 8, the distinctive quasiparticle distributionexisting in the N region of a biased SINIS structure ~where Istands for an insulating barrier! is also well suited to controlthe Josephson coupling in a long SNS weak link, allowingeither large supercurrent enhancement or efficient suppres-sion with respect to equilibrium.In this letter, we present the implementation and charac-terization of a four-terminal superconducting structure ~seeFig. 1! consisting of a SNS mesoscopic junction integratedwith a SINIS electron cooler. A similar device was consid-ered but not successfully operated in Ref. 7. In this transistor,the maximum supercurrent flowing in the SNS junction iscontrolled by voltage biasing the SINIS line whose N regionis shared with the Josephson junction. Low temperaturetransport measurements show enhancement of the criticalcurrent under hot quasiparticle extraction by more than afactor of two with respect to equilibrium. In addition thisdevice demonstrates low power dissipation and large currentgain.The sample ~shown in Fig. 1! consists of a Cu island,0.37 mm wide and 30 nm thick, symmetrically connected atits ends via insulating barriers ~with normal-state resistanceRT.240 V! to two 60-nm-thick Al reservoirs, thus realizinga SINIS cooler. The Josephson junction instead consists of anAl/Cu/Al SNS weak link ~with normal-state resistanceRN511.5 V!, whose N region is shared with the SINIS line.The minimum interelectrode separation in the SNS junctionof the present device is LJ.0.4 mm. The structure was fab-ricated on a thermally oxidized Si substrate by electron beamlithography and three-angle shadow-mask evaporation. Theelectrical characterization was performed at different bathtemperatures down to 70 mK in a dilution refrigerator. Fromlow-temperature resistance measurements we deduced theCu diffusion coefficient D’10 cm2/s. This low value of Dis probably caused by significant intermixing of the materialsat the NS interface leading to the strong reduction of theelectron mean free path in the weak link. The Al energy gap,D5169 meV, was inferred from the low-temperaturecurrent–voltage characteristic of the SINIS line ~see Fig. 4!.The coherence length jN5A\D/D’62 nm is then muchsmaller than LJ , providing the frame of the long junctionregime.The experiment consists of sweeping the ISNS currentacross the SNS junction while measuring its differential re-a!Electronic mail: savin@boojum.hut.flFIG. 1. Scanning electron micrograph of a typical structure including asketch of the measurement circuit. Two superconducting Al electrodes areconnected through insulating barriers to a Cu island to realize a symmetricSINIS electron cooler. The supercurrent IJ in the Al/Cu/Al junction is tunedupon voltage biasing the SINIS control line.APPLIED PHYSICS LETTERS VOLUME 84, NUMBER 21 24 MAY 200441790003-6951/2004/84(21)/4179/3/$22.00 © 2004 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Wed, 20 May 2015 03:48:10sistance dV/dI at different values of voltage bias (VSINIS)across the SINIS control line. Figure 2~a! shows a subset ofdV/dI vs ISNS characteristics measured at the bath tempera-ture Tbath572 mK for several VSINIS . The curves display anonhysteretic behavior characteristic for overdampedjunctions.9 In the case of a SNS weak link the effect ofthermal fluctuations on the smearing of the voltage–currentcharacteristic is stronger10 than predicted by the model forresistively shunted junction.11 We have chosen to define theexperimental critical current as the current where the differ-ential resistance reaches RN/2.12 Notably, upon increasingVSINIS , the current range where the differential resistancevanishes widens initially, thus reflecting an enhancement ofIJ , being maximized at a voltage corresponding to VSINIS5300 mV.1.8D/e13 @curve labeled as 3 in Fig. 2~a!#; then,further increase of bias leads to a monotonic decay and to acomplete suppression of IJ at larger voltages @curve labeledas 6 in Fig. 2~a!#. This nonmonotonic behavior is seen in thecorresponding I – V curves in Fig. 2~b!.The observed behavior is due to the relation existingbetween the observable maximum supercurrent IJ and thequasiparticle energy distribution in the weak link. In thepresent experimental situation of large LSINIS , inelasticelectron–electron relaxation forces the electron system to re-tain a local thermal ~quasi!equilibrium. As a consequence,the quasiparticle energy distribution can be described with aFermi–Dirac function at an effective electron temperatureTe . The temperature Te is determined by the balance be-tween two heat flows:P~VSINIS ,Te ,Tbath!1Pe2bath~Te ,Tbath!50. ~1!The first term accounts for the net heat current P transferredfrom the N island to the superconductors upon biasing theSINIS line:13P5 2e2RTE2‘‘n~E !@ f 0~E˜ ,Te!2 f 0~E ,Tbath!#E˜ dE , ~2!where E˜ 5E2eVSINIS/2, f 0(E ,T) is the Fermi–Dirac distri-bution function and n(E)5uRe@(E1iG)/A(E1iG)22D2#u isthe ~smeared by nonzero G! BCS density of states of thesuperconductor.15 Equation ~2! is symmetric in VSINIS , beingmaximized slightly below u2D/eu. The second term accountsfor energy transfer from electrons to the phonons of the nor-mal island at the temperature Tbath and is equal to Pe2bath5SV(Te52Tbath5 ),16 where V is the volume of the N islandand S’2 nWK25 mm23 for copper.13 The temperature Te inthe weak link thus strongly depends on VSINIS and can besmaller than Tbath .17 At low temperature ~i.e., kBTbath!D!, ina long SNS junction, IJ is predicted to decrease exponen-tially as Te increases18 in the regime where kBTe@ETh5\D/LJ2. Thus, upon biasing the SINIS line, IJ will bechanged with respect to equilibrium ~i.e., at VSINIS50!, dueto the modification of Te that now differs from Tbath .In Fig. 3~a! we plot the extracted IJ values as a functionof VSINIS at three different bath temperatures. For all dis-played temperatures, the critical current increases monotoni-cally up to about VSINIS.1.8D/e as expected from the reduc-tion of Te by cooling. Then, further increase of bias voltageleads to an efficient supercurrent suppression due to electronheating. The equilibrium critical current ~i.e., at VSINIS50! vsTbath is displayed in Fig. 3~b!. The IJ behavior follows acharacteristic trend, decreasing upon rising the temperature,but it differs from the temperature dependence predicted byquasiclassical Green-function theory.1 The discrepancy canbe ascribed to the uncertainty in the determination of theactual values of critical current, relatively narrow tempera-ture range where it was observed and thermal decouplingbetween electrons and bath at temperatures below 200 mK.In Fig. 3, we show the expected critical current dependenceon VSINIS at Tbath5283 mK obtained from the solution ofEqs. ~1! and ~2! to determine the effective electron tempera-ture Te upon biasing the SINIS line, and assuming a linearbehavior of the critical current IJ vs Te below about 350 mK,the slope of the linear dependence being inferred from themeasured IJ(Tbath). For this calculation, we assumed the al-ready given parameters for the SINIS line and G51.831023D estimated from the ratio ~.G/D! of the low-temperature SINIS conductance at low and high bias.14 TheFIG. 2. Selected dV/dI vs ISNS ~a! and current–voltagecharacteristics ~b! of the SNS junction at Tbath572 mKfor different VSINIS values ~all curves are offset for clar-ity!: 1–0, 2–194 mV, 3–300 mV, 4–342 mV, 5–355 mV,6–938 mV. Curves in ~b! were obtained by numericalintegration of the corresponding ones in ~a!.FIG. 3. ~a! Critical current IJ vs control voltage VSINIS at three different bathtemperatures; ~b! equilibrium supercurrent (VSINIS50) vs bath temperature.Dashed line in ~a! represents curve obtained from energy balance Eq. ~1!and the linear approximation of IJ(Tbath) shown in ~b!.4180 Appl. Phys. Lett., Vol. 84, No. 21, 24 May 2004 Savin et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Wed, 20 May 2015 03:48:10resemblance between calculation and experiment is evidentalthough details of the former one are dictated by the IJdependence on temperature, which we cannot extrapolate re-liably. To better characterize our device, we show in Fig. 4~right axis! the dissipated power P against VSINIS in the SI-NIS line at Tbath572 mK. The plot reveals that in the biasvoltage region of significant critical current enhancement~i.e., in the 200–300 mV bias range! P obtains values of theorder of 10213 W, while in the regime of supercurrent sup-pression ~i.e., for VSINIS.300 mV! some tens of pW. Thisdemonstrates the low power dissipation intrinsic to thestructure.8 The P behavior is directly related to the normalcurrent flow in the control line. The latter is displayed on theleft-hand side axis of Fig. 4 and shows that control currentsas low as a few nA are necessary to enhance the criticalcurrent, while of about 100 nA to suppress it. The differentialcurrent gain GI5dIJ /dISINIS against ISINIS is shown in theinset of Fig. 4. Notably, GI obtains values exceeding 20 inthe hot quasiparticle extraction regime, while of about 211in the voltage region of supercurrent suppression. We notethat higher GI values, as well as lower power dissipation andcontrol currents, could be attained by optimizing the struc-ture design.8,14In summary, we have demonstrated experimentally con-trol of Josephson coupling under hot quasiparticle extractionin a four-terminal superconducting structure. Our experimen-tal result shows the potential of a SINIS line as a basis of apromising class of mesoscopic transistors with high currentgain.The authors acknowledge T. T. Heikkila¨, F. Carillo, R.Fazio, P. J. Hakonen, F. W. J. Hekking, and F. Taddei fordiscussions, and Academy of Finland for financial support~TULE Program!. One of the authors ~F.G.! would like toacknowledge the Large Scale Installation Program ULTI-3 ofthe European Union for the kind hospitality and for financialsupport.1 W. Belzig, F. K. Wilhelm, C. Bruder, G. Scho¨n, and A. D. Zaikin, Super-lattices Microstruct. 25, 1251 ~1999!.2 C. J. Lambert and R. Raimondi, J. Phys.: Condens. Matter 10, 901 ~1998!.3 A. F. Andreev, Zh. Eksp. Teor. Fiz. 46, 1823 ~1964!.4 F. K. Wilhelm, G. Scho¨n, and A. D. Zaikin, Phys. Rev. Lett. 81, 1682~1998!; A. F. Volkov, ibid. 74, 4730 ~1995!; S.-K. Yip, Phys. Rev. B 58,5803 ~1998!.5 A. F. Morpurgo, T. M. Klapwijk, and B. J. van Wees, Appl. Phys. Lett. 72,966 ~1998!.6 J. J. A. Baselmans, A. F. Morpurgo, B. J. van Wees, and T. M. Klapwijk,Nature ~London! 397, 43 ~1999!; R. Shaikhaidarov, A. F. Volkov, H.Takayanagi, V. T. Petrashov, and P. Delsing, Phys. Rev. B 62, R14649~2000!; J. Huang, F. Pierre, T. T. Heikkila¨, F. K. Wilhelm, and N. O. Birge,ibid. 66, 020507 ~2002!.7 J. J. A. Baselmans, Ph.D. thesis, University of Groningen, The Nether-lands, 2002.8 F. Giazotto, F. Taddei, T. T. Heikkila¨, R. Fazio, and F. Beltram, Appl.Phys. Lett. 83, 2877 ~2003!.9 K. K. Likharev, Rev. Mod. Phys. 51, 101 ~1979!.10 T. Hoss, C. Strunk, T. Nussbaumer, R. Huber, U. Staufer, and C. Scho¨nen-berger, Phys. Rev. B 62, 4079 ~2000!.11 V. Ambegaokar and B. I. Halperin, Phys. Rev. Lett. 22, 1364 ~1969!.12 P. Dubos, H. Courtois, B. Pannetier, F. K. Wilhelm, A. D. Zaikin, and G.Scho¨n, Phys. Rev. B 63, 064502 ~2001!.13 M. M. Leivo, J. P. Pekola, and D. V. Averin, Appl. Phys. Lett. 68, 1996~1996!.14 J. P. Pekola, T. T. Heikkila¨, A. M. Savin, J. T. Flyktman, F. Giazotto, andF. W. J. Hekking, Phys. Rev. Lett. 92, 056804 ~2004!.15 The parameter G allows quasiparticle states within the energy gap D ~Ref.14!.16 F. C. Wellstood, C. Urbina, and J. Clarke, Phys. Rev. B 49, 5942 ~1994!.17 M. L. Roukes, M. R. Freeman, R. S. Germain, and R. C. Richardson,Phys. Rev. Lett. 55, 422 ~1985!.18 A. D. Zaikin and G. F. Zharkov, Sov. J. Low Temp. Phys. 7, 184 ~1981!;F. K. Wilhelm, A. D. Zaikin, and G. Scho¨n, J. Low Temp. Phys. 106, 305~1997!.FIG. 4. Current-voltage characteristic ~left axis! and power dissipation P5VSINISISINIS ~right axis! of the SINIS line at Tbath572 mK. The inset showsthe measured differential current gain GI against ISINIS at the same tempera-ture ~also displayed is the dependence on VSINIS).4181Appl. Phys. Lett., Vol. 84, No. 21, 24 May 2004 Savin et al. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:130.233.216.27 On: Wed, 20 May 2015 03:48:10

Savin, Alexander

Pekola, Jukka

Flyktman, J.T.

Aaltodoc

Anthore, Anne

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s): Savin, A. M. & Pekola, Jukka & Flyktman, J. T. & Anthore, A. &
Giazotto, F.
Title: Cold electron Josephson transistor
Year: 2004
Version: Final published version
Please cite the original version:
Savin, A. M. & Pekola, Jukka & Flyktman, J. T. & Anthore, A. & Giazotto, F. 2004. Cold
electron Josephson transistor. Applied Physics Letters. Volume 84, Issue 21. P.
4179-4181. ISSN 0003-6951 (printed). DOI: 10.1063/1.1756192.
Rights: © 2004 American Institute of Physics. This article may be downloaded for personal use only. Any other use
requires prior permission of the author and the American Institute of Physics. The following article appeared
in Applied Physics Letters and may be found at
http://scitation.aip.org/content/aip/journal/apl/84/21/10.1063/1.1756192
All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and
duplication or sale of all or part of any of the repository collections is not permitted, except that material may
be duplicated by you for your research use or educational purposes in electronic or print form. You must
obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or
otherwise to anyone who is not an authorised user.
Powered by TCPDF (www.tcpdf.org)
Cold electron Josephson transistor
A. M. Savin, J. P. Pekola, J. T. Flyktman, A. Anthore, and F. Giazotto 
 
Citation: Applied Physics Letters 84, 4179 (2004); doi: 10.1063/1.1756192 
View online: http://dx.doi.org/10.1063/1.1756192 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/84/21?ver=pdfcov 
Published by the AIP Publishing 
 
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Appl. Phys. Lett. 103, 092601 (2013); 10.1063/1.4819461 
 
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Appl. Phys. Lett. 87, 092502 (2005); 10.1063/1.2034096 
 
Charge and spin effects in mesoscopic Josephson junctions (Review) 
Low Temp. Phys. 30, 554 (2004); 10.1063/1.1789291 
 
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 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.27 On: Wed, 20 May 2015 03:48:10
Cold electron Josephson transistor
A. M. Savin,a) J. P. Pekola, J. T. Flyktman, and A. Anthore
Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland
F. Giazotto
NEST-INFM and Scuola Normale Superiore, I-56126 Pisa, Italy
~Received 20 February 2004; accepted 7 April 2004; published online 6 May 2004!
A superconductor-normal metal-superconductor mesoscopic Josephson junction has been realized in
which the critical current is tuned through normal current injection using a symmetric electron
cooler directly connected to the weak link. Both enhancement of the critical current by more than
a factor of two, and supercurrent suppression have been achieved by varying the cooler bias.
Furthermore, this transistor-like device demonstrates large current gain ~;20! and low power
dissipation. © 2004 American Institute of Physics. @DOI: 10.1063/1.1756192#
Transport dynamics in mesoscopic structures where nor-
mal metals ~N! are coupled with superconductors ~S! are
currently the focus of extensive research.1,2 This stems
mainly from the relevance these systems have both from the
fundamental physics point of view and in light of their pos-
sible exploitation in nanoelectronics. In diffusive SNS junc-
tions, where the length of the N region exceeds the elastic
mean free path, coherent sequential Andreev scattering3 be-
tween the superconductors may lead to a continuum spec-
trum of resonant levels1 responsible for carrying the super-
current flow through the structure. The Josephson current is
given by supercurrent spectrum weighted by the occupation
number of correlated electron-hole pairs that is determined
by the quasiparticle energy distribution in the N region of the
junction. By changing the latter through current injection
from additional nonsuperconducting terminals connected to
the N region4 both supercurrent suppression5 as well as its
sign reversal ~p-transition! were demonstrated.6 As predicted
in Refs. 7 and 8, the distinctive quasiparticle distribution
existing in the N region of a biased SINIS structure ~where I
stands for an insulating barrier! is also well suited to control
the Josephson coupling in a long SNS weak link, allowing
either large supercurrent enhancement or efficient suppres-
sion with respect to equilibrium.
In this letter, we present the implementation and charac-
terization of a four-terminal superconducting structure ~see
Fig. 1! consisting of a SNS mesoscopic junction integrated
with a SINIS electron cooler. A similar device was consid-
ered but not successfully operated in Ref. 7. In this transistor,
the maximum supercurrent flowing in the SNS junction is
controlled by voltage biasing the SINIS line whose N region
is shared with the Josephson junction. Low temperature
transport measurements show enhancement of the critical
current under hot quasiparticle extraction by more than a
factor of two with respect to equilibrium. In addition this
device demonstrates low power dissipation and large current
gain.
The sample ~shown in Fig. 1! consists of a Cu island,
0.37 mm wide and 30 nm thick, symmetrically connected at
its ends via insulating barriers ~with normal-state resistance
RT.240 V! to two 60-nm-thick Al reservoirs, thus realizing
a SINIS cooler. The Josephson junction instead consists of an
Al/Cu/Al SNS weak link ~with normal-state resistance
RN511.5 V!, whose N region is shared with the SINIS line.
The minimum interelectrode separation in the SNS junction
of the present device is LJ.0.4 mm. The structure was fab-
ricated on a thermally oxidized Si substrate by electron beam
lithography and three-angle shadow-mask evaporation. The
electrical characterization was performed at different bath
temperatures down to 70 mK in a dilution refrigerator. From
low-temperature resistance measurements we deduced the
Cu diffusion coefficient D’10 cm2/s. This low value of D
is probably caused by significant intermixing of the materials
at the NS interface leading to the strong reduction of the
electron mean free path in the weak link. The Al energy gap,
D5169 meV, was inferred from the low-temperature
current–voltage characteristic of the SINIS line ~see Fig. 4!.
The coherence length jN5A\D/D’62 nm is then much
smaller than LJ , providing the frame of the long junction
regime.
The experiment consists of sweeping the ISNS current
across the SNS junction while measuring its differential re-
a!Electronic mail: savin@boojum.hut.fl
FIG. 1. Scanning electron micrograph of a typical structure including a
sketch of the measurement circuit. Two superconducting Al electrodes are
connected through insulating barriers to a Cu island to realize a symmetric
SINIS electron cooler. The supercurrent IJ in the Al/Cu/Al junction is tuned
upon voltage biasing the SINIS control line.
APPLIED PHYSICS LETTERS VOLUME 84, NUMBER 21 24 MAY 2004
41790003-6951/2004/84(21)/4179/3/$22.00 © 2004 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
130.233.216.27 On: Wed, 20 May 2015 03:48:10
sistance dV/dI at different values of voltage bias (VSINIS)
across the SINIS control line. Figure 2~a! shows a subset of
dV/dI vs ISNS characteristics measured at the bath tempera-
ture Tbath572 mK for several VSINIS . The curves display a
nonhysteretic behavior characteristic for overdamped
junctions.9 In the case of a SNS weak link the effect of
thermal fluctuations on the smearing of the voltage–current
characteristic is stronger10 than predicted by the model for
resistively shunted junction.11 We have chosen to define the
experimental critical current as the current where the differ-
ential resistance reaches RN/2.12 Notably, upon increasing
VSINIS , the current range where the differential resistance
vanishes widens initially, thus reflecting an enhancement of
IJ , being maximized at a voltage corresponding to VSINIS
5300 mV.1.8D/e13 @curve labeled as 3 in Fig. 2~a!#; then,
further increase of bias leads to a monotonic decay and to a
complete suppression of IJ at larger voltages @curve labeled
as 6 in Fig. 2~a!#. This nonmonotonic behavior is seen in the
corresponding I – V curves in Fig. 2~b!.
The observed behavior is due to the relation existing
between the observable maximum supercurrent IJ and the
quasiparticle energy distribution in the weak link. In the
present experimental situation of large LSINIS , inelastic
electron–electron relaxation forces the electron system to re-
tain a local thermal ~quasi!equilibrium. As a consequence,
the quasiparticle energy distribution can be described with a
Fermi–Dirac function at an effective electron temperature
Te . The temperature Te is determined by the balance be-
tween two heat flows:
P~VSINIS ,Te ,Tbath!1Pe2bath~Te ,Tbath!50. ~1!
The first term accounts for the net heat current P transferred
from the N island to the superconductors upon biasing the
SINIS line:13
P5 2
e2RT
E
2‘
‘
n~E !@ f 0~E˜ ,Te!2 f 0~E ,Tbath!#E˜ dE , ~2!
where E˜ 5E2eVSINIS/2, f 0(E ,T) is the Fermi–Dirac distri-
bution function and n(E)5uRe@(E1iG)/A(E1iG)22D2#u is
the ~smeared by nonzero G! BCS density of states of the
superconductor.15 Equation ~2! is symmetric in VSINIS , being
maximized slightly below u2D/eu. The second term accounts
for energy transfer from electrons to the phonons of the nor-
mal island at the temperature Tbath and is equal to Pe2bath
5SV(Te52Tbath5 ),16 where V is the volume of the N island
and S’2 nWK25 mm23 for copper.13 The temperature Te in
the weak link thus strongly depends on VSINIS and can be
smaller than Tbath .17 At low temperature ~i.e., kBTbath!D!, in
a long SNS junction, IJ is predicted to decrease exponen-
tially as Te increases18 in the regime where kBTe@ETh
5\D/LJ
2
. Thus, upon biasing the SINIS line, IJ will be
changed with respect to equilibrium ~i.e., at VSINIS50!, due
to the modification of Te that now differs from Tbath .
In Fig. 3~a! we plot the extracted IJ values as a function
of VSINIS at three different bath temperatures. For all dis-
played temperatures, the critical current increases monotoni-
cally up to about VSINIS.1.8D/e as expected from the reduc-
tion of Te by cooling. Then, further increase of bias voltage
leads to an efficient supercurrent suppression due to electron
heating. The equilibrium critical current ~i.e., at VSINIS50! vs
Tbath is displayed in Fig. 3~b!. The IJ behavior follows a
characteristic trend, decreasing upon rising the temperature,
but it differs from the temperature dependence predicted by
quasiclassical Green-function theory.1 The discrepancy can
be ascribed to the uncertainty in the determination of the
actual values of critical current, relatively narrow tempera-
ture range where it was observed and thermal decoupling
between electrons and bath at temperatures below 200 mK.
In Fig. 3, we show the expected critical current dependence
on VSINIS at Tbath5283 mK obtained from the solution of
Eqs. ~1! and ~2! to determine the effective electron tempera-
ture Te upon biasing the SINIS line, and assuming a linear
behavior of the critical current IJ vs Te below about 350 mK,
the slope of the linear dependence being inferred from the
measured IJ(Tbath). For this calculation, we assumed the al-
ready given parameters for the SINIS line and G51.8
31023D estimated from the ratio ~.G/D! of the low-
temperature SINIS conductance at low and high bias.14 The
FIG. 2. Selected dV/dI vs ISNS ~a! and current–voltage
characteristics ~b! of the SNS junction at Tbath572 mK
for different VSINIS values ~all curves are offset for clar-
ity!: 1–0, 2–194 mV, 3–300 mV, 4–342 mV, 5–355 mV,
6–938 mV. Curves in ~b! were obtained by numerical
integration of the corresponding ones in ~a!.
FIG. 3. ~a! Critical current IJ vs control voltage VSINIS at three different bath
temperatures; ~b! equilibrium supercurrent (VSINIS50) vs bath temperature.
Dashed line in ~a! represents curve obtained from energy balance Eq. ~1!
and the linear approximation of IJ(Tbath) shown in ~b!.
4180 Appl. Phys. Lett., Vol. 84, No. 21, 24 May 2004 Savin et al.
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resemblance between calculation and experiment is evident
although details of the former one are dictated by the IJ
dependence on temperature, which we cannot extrapolate re-
liably. To better characterize our device, we show in Fig. 4
~right axis! the dissipated power P against VSINIS in the SI-
NIS line at Tbath572 mK. The plot reveals that in the bias
voltage region of significant critical current enhancement
~i.e., in the 200–300 mV bias range! P obtains values of the
order of 10213 W, while in the regime of supercurrent sup-
pression ~i.e., for VSINIS.300 mV! some tens of pW. This
demonstrates the low power dissipation intrinsic to the
structure.8 The P behavior is directly related to the normal
current flow in the control line. The latter is displayed on the
left-hand side axis of Fig. 4 and shows that control currents
as low as a few nA are necessary to enhance the critical
current, while of about 100 nA to suppress it. The differential
current gain GI5dIJ /dISINIS against ISINIS is shown in the
inset of Fig. 4. Notably, GI obtains values exceeding 20 in
the hot quasiparticle extraction regime, while of about 211
in the voltage region of supercurrent suppression. We note
that higher GI values, as well as lower power dissipation and
control currents, could be attained by optimizing the struc-
ture design.8,14
In summary, we have demonstrated experimentally con-
trol of Josephson coupling under hot quasiparticle extraction
in a four-terminal superconducting structure. Our experimen-
tal result shows the potential of a SINIS line as a basis of a
promising class of mesoscopic transistors with high current
gain.
The authors acknowledge T. T. Heikkila¨, F. Carillo, R.
Fazio, P. J. Hakonen, F. W. J. Hekking, and F. Taddei for
discussions, and Academy of Finland for financial support
~TULE Program!. One of the authors ~F.G.! would like to
acknowledge the Large Scale Installation Program ULTI-3 of
the European Union for the kind hospitality and for financial
support.
1 W. Belzig, F. K. Wilhelm, C. Bruder, G. Scho¨n, and A. D. Zaikin, Super-
lattices Microstruct. 25, 1251 ~1999!.
2 C. J. Lambert and R. Raimondi, J. Phys.: Condens. Matter 10, 901 ~1998!.
3 A. F. Andreev, Zh. Eksp. Teor. Fiz. 46, 1823 ~1964!.
4 F. K. Wilhelm, G. Scho¨n, and A. D. Zaikin, Phys. Rev. Lett. 81, 1682
~1998!; A. F. Volkov, ibid. 74, 4730 ~1995!; S.-K. Yip, Phys. Rev. B 58,
5803 ~1998!.
5 A. F. Morpurgo, T. M. Klapwijk, and B. J. van Wees, Appl. Phys. Lett. 72,
966 ~1998!.
6 J. J. A. Baselmans, A. F. Morpurgo, B. J. van Wees, and T. M. Klapwijk,
Nature ~London! 397, 43 ~1999!; R. Shaikhaidarov, A. F. Volkov, H.
Takayanagi, V. T. Petrashov, and P. Delsing, Phys. Rev. B 62, R14649
~2000!; J. Huang, F. Pierre, T. T. Heikkila¨, F. K. Wilhelm, and N. O. Birge,
ibid. 66, 020507 ~2002!.
7 J. J. A. Baselmans, Ph.D. thesis, University of Groningen, The Nether-
lands, 2002.
8 F. Giazotto, F. Taddei, T. T. Heikkila¨, R. Fazio, and F. Beltram, Appl.
Phys. Lett. 83, 2877 ~2003!.
9 K. K. Likharev, Rev. Mod. Phys. 51, 101 ~1979!.
10 T. Hoss, C. Strunk, T. Nussbaumer, R. Huber, U. Staufer, and C. Scho¨nen-
berger, Phys. Rev. B 62, 4079 ~2000!.
11 V. Ambegaokar and B. I. Halperin, Phys. Rev. Lett. 22, 1364 ~1969!.
12 P. Dubos, H. Courtois, B. Pannetier, F. K. Wilhelm, A. D. Zaikin, and G.
Scho¨n, Phys. Rev. B 63, 064502 ~2001!.
13 M. M. Leivo, J. P. Pekola, and D. V. Averin, Appl. Phys. Lett. 68, 1996
~1996!.
14 J. P. Pekola, T. T. Heikkila¨, A. M. Savin, J. T. Flyktman, F. Giazotto, and
F. W. J. Hekking, Phys. Rev. Lett. 92, 056804 ~2004!.
15 The parameter G allows quasiparticle states within the energy gap D ~Ref.
14!.
16 F. C. Wellstood, C. Urbina, and J. Clarke, Phys. Rev. B 49, 5942 ~1994!.
17 M. L. Roukes, M. R. Freeman, R. S. Germain, and R. C. Richardson,
Phys. Rev. Lett. 55, 422 ~1985!.
18 A. D. Zaikin and G. F. Zharkov, Sov. J. Low Temp. Phys. 7, 184 ~1981!;
F. K. Wilhelm, A. D. Zaikin, and G. Scho¨n, J. Low Temp. Phys. 106, 305
~1997!.
FIG. 4. Current-voltage characteristic ~left axis! and power dissipation P
5VSINISISINIS ~right axis! of the SINIS line at Tbath572 mK. The inset shows
the measured differential current gain GI against ISINIS at the same tempera-
ture ~also displayed is the dependence on VSINIS).
4181Appl. Phys. Lett., Vol. 84, No. 21, 24 May 2004 Savin et al.
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Cold electron Josephson transistor

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