Current-voltage characteristics of Pb and Sn granular superconducting nanowires

Article abstract of DOI:10.1063/1.1582356

Current-voltage characteristics of Pb and Sn granular superconducting nanowires were investigated. The nanowires were prepared by electrodeposition in nanoporous membranes. It was observed that phase-slip-centers were formed far below the critical tempera

Full text of DOI:10.1063/1.1582356

Current–voltage characteristics of Pb and Sn granular superconducting
nanowires
Sébastien Michotte, Stefan Mátéfi-Tempfli, and Luc Piraux
Citation: Appl. Phys. Lett. 82, 4119 (2003); doi: 10.1063/1.1582356
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APPLIED PHYSICS LETTERS
VOLUME 82, NUMBER 23
9 JUNE 2003
Current–voltage characteristics of Pb and Sn granular superconducting
nanowires
a)
S e´ bastien Michotte, Stefan M a´ t e´ fi-Tempfli, and Luc Piraux
Unit e´ de Physico-Chimie et de Physique des Mat e´ riaux (PCPM), Universit e´ Catholique de Louvain,
Place Croix du Sud 1, B-1348 Louvain-la-Neuve, Belgium and Research Center on Microscopic
and Nanoscopic Electronic Devices and Materials (CERMIN), Universit e´ Catholique de Louvain,
B-1348 Louvain-La-Neuve, Belgium
͑
Received 10 December 2002; accepted 23 April 2003͒
Arrays of granular superconducting Pb and Sn nanowires ͑40–55 nm in diameter and 22 or 50 ␮m
long͒ have been prepared by electrodeposition in nanoporous membranes. A simple technique has
been developed to perform electrical transport measurement on a single nanowire. By sweeping the
dc current inside the nanowire, we observed the formation of phase-slip-centers far below the
critical temperature. In contrast, in voltage-driven experiments, an interesting S-shaped behavior has
been observed in the nucleation region of these phase-slip-centers. © 2003 American Institute of
Physics. ͓DOI: 10.1063/1.1582356͔
It has been known for a few decades that a critical cur-
AgCl reference electrode was used in a three-electrode con-
figuration in order to reduce the Pb2 or Sn ions into the
pores. As can be seen on nanowires prepared from the same
membrane and under the same conditions ͑Fig. 1͒, the
nanowires are cylindrical and the diameter is uniform along
their length.
ϩ
2ϩ
rent I only perturbs, not suppresses, superconductivity in a
c
sample of low dimensionality. Instead of depinning the vor-
tex array ͑as for a type-II bulk superconductor͒ and finally
turning the sample normal, this current induces a nonequilib-
rium phenomenon and leads to the successive nucleation of
phase-slip-centers ͑PSCs͒ arising from Josephson-like pulsa-
tions. This behavior was first observed with conventional
In order to perform electrical transport measurements on
a single nanowire, a self-contacting technique has been de-
veloped ͓Fig. 2͑a͔͒. In addition to the thick gold cathode ͑ϳ1
superconductors in the form of whiskers or microbridges,3
1,2
␮m͒ from which the nanowires start to grow up inside the
but it is also present, for example, in thin films of conven-
membrane, another thin gold layer ͑in the range of 50 to 200
nm͒ was deposited on the other side exposed to the electro-
lyte prior to electrodeposition. This contacting layer covers
the surface, but, contrary to the cathode, it is not thick
enough to plug the pores. As for these small pore diameters
the nanowires do not grow at the same speed, the first emerg-
ing nanowire interrupts the growth of the others by favoring
the formation of a film of the deposited material on this
contacting layer. This electrodeposited film also presents the
tional
superconductors
or
high-temperature
4
superconductors, and thus it always generates a lot of inter-
est. The simplest geometry to study these PSCs is a one-
dimensional ͑1D͒ superconductor having a diameter smaller
than the coherence length, which is thus too narrow to ac-
commodate a single vortex and where these PSCs can be
viewed as the substitute to the vortex flow process. However,
the previous studies on whiskers and microbridges in this 1D
regime did not allow observation of PSCs far below T be-
c
cause the increased power dissipation produces local heating.
For TϪT տ0.1 K, the PSC nucleation was hidden by fully
c
5
normal spreading hot-spots, even when a weak spot was
deliberately introduced to depress I , which lowers the heat
c
6
dissipation. In contrast, our nanowire system presents the
advantage to remain in this 1D regime even far below Tc ,
and the heating level is sufficiently low to allow the obser-
vation of these PSCs.
The superconducting nanowires were prepared by elec-
trodeposition into the nanopores of homemade track-etched
7
polycarbonate membranes. For the lead nanowires, a 22-
␮
m-thick membrane ͑with pore diameter ϳ40 nm and pore
9
Ϫ2
density ϳ4ϫ10 cm ) and an aqueous solution of 40.4 g/l
Pb(BF ) , 33.6 g/l HBF , and 15 g/l H BO were used. In
8
,9
4
2
4
3
3
the case of tin nanowires, a 50-␮m-thick membrane ͑with
9
Ϫ2
pore diameter ϳ55 nm and pore density ϳ2ϫ10 cm
)
and an electrolyte of 41.8 g/l Sn(BF4)2 in water solution
were used. A constant potential of Ϫ0.5 V versus an Ag/
FIG. 1. Scanning electron microscopy-field emission gun ͑SEM-FEG͒ mi-
crograph of lead nanowires after dissolution of the hosting polycarbonate
membrane with dichloromethane.
a͒Electronic mail: michotte@pcpm.ucl.ac.be
0003-6951/2003/82(23)/4119/3/$20.00
4119
© 2003 American Institute of Physics
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4120
Appl. Phys. Lett., Vol. 82, No. 23, 9 June 2003
Michotte, M a´ t e´ fi-Tempfli, and Piraux
FIG. 2. ͑a͒ Schematic drawing of the
sample illustrating the self-contacting
technique and SEM-FEG micrographs
of the membrane and the gold contact-
ing layer. ͑b͒ R(T) of a Pb nanowire
͑
40 nm in diameter, 22 ␮m long͒ and
of a Sn nanowire ͑55 nm in diameter,
0 ␮m long͒ measured with a lock-in
5
amplifier by applying a small current
of 0.1 ␮A.
advantage of perfect encapsulation of the nanowire inside the
membrane, insuring protection against oxidation.
successive appearance of two PSCs at low temperature ͑e.g.,
at Iϭ50 and 63 ␮A, respectively, at Tϭ4.3 K). According to
the phenomenological Skocpol–Beasley–Tinkham ͑SBT͒
All the transport measurements were done in an electro-
magnetically shielded environment. Our cryostat was ad-
equately grounded and filtered. Low-noise triax connectors
and cables were used as well as Keithley sources and volt-
meters. The low-temperature resistance of a 40-nm Pb nano-
wire ͑22 ␮m long͒ and a 55-nm Sn nanowire ͑50 ␮m long͒ is
shown in Fig. 2͑b͒. The critical temperature is not far from
its bulk value: 7.2 K for lead and 3.7 K for tin. From the
numerous measurements performed both on Pb and on Sn
3
model, on time average, 65% of total current is supercon-
nanowires, it appears that only small depressions of T were
c
observed. In addition, a superconducting transition was
found to occur when the residual resistivity ratio RRR is
larger than about 2, while for smaller RRR values, an insu-
lating behavior is observed. Therefore, our nanowires are in
the granular limit and moreover are moderately disordered:
in the present study, the RRR of the samples was larger than
10. Structural characterization of the Pb nanowires using
transmission-electron-microscopy ͑TEM͒ experiments con-
firms also this granular character.8 In this context, the
T-independent resistance far below T could be a signature
c
of the metallic part of the superconductor–metal–insulator
͑
S–M–I͒ transition10 although the contribution from the con-
tact resistance can hardly be subtracted. Moreover, in granu-
lar superconductors, disorder favors quantum fluctuations of
the phase of the order parameter, rather than suppression of
the amplitude of this order parameter. This is why only small
depressions of T were observed.
c
In Fig. 3, the dc voltage–current characteristics of the Pb
and Sn nanowires are reported, applying either a dc current
or a dc voltage. In the two types of experiments, no hyster-
esis was observed. These measurements were also performed
with reversed polarity, without any change in the results. In
the current-driven experiment, which is the one usually per-
formed, we observe for the Pb nanowire in Fig. 3͑a͒, the
FIG. 3. Voltage–current characteristics at different temperatures of ͑a͒ a Pb
nanowire ͑40 nm in diameter, 22 ␮m long͒ and ͑b͒ a Sn nanowire ͑55 nm in
diameter, 50 ␮m long͒. Open arrow, the dc voltage measured versus the
applied dc current ͑I-drive͒. Filled arrow, the dc current through the nano-
wire versus the applied dc voltage (V-drive͒.
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Appl. Phys. Lett., Vol. 82, No. 23, 9 June 2003
Michotte, M a´ t e´ fi-Tempfli, and Piraux
4121
ducting inside a PSC. The size of the first PSC can then be
estimated from the ratio of the first voltage jump to the total
corresponding normal voltage for a 22-␮m-long nanowire.
The value thus estimated ͑18 ␮m͒ is reasonable because it is
twice the quasiparticle’s diffusion length, which is typically
of the order of 10 ␮m in such a superconductor. Despite the
fact that successive PSCs tend to avoid those already in
place, the second PSC created in this Pb nanowire is thus
forced to interpenetrate the first one, which explains why the
second jump in resistance is smaller. The current-driven ex-
periment on the 50-␮m-long Sn nanowire in Fig. 3͑b͒ also
shows the formation a PSC at low temperature, but for this
particular material, the PSC extension is larger ͑around 40
high density of nanopores ͓see Fig. 2͑a͔͒. These other
nanowires are not contacted electrically to the contacting
layer, but they also contribute to heat transfer in the compos-
ite material due to their large thermal conductivity. The
bending of the curve seen for the largest currents of Fig. 3͑a͒
is a signature of heating effects in the measurements of the
Pb nanowire. It should, however, be emphasized that this
effect is almost negligible in the experiment involving the Sn
nanowire ͓Fig. 3͑b͔͒, likely due to a smaller contact resis-
tance and/or better heat evacuation. As a consequence, al-
though the exact shape of the reported S-behavior for the Pb
nanowire is probably slightly modified due to the tempera-
ture increase, the heating effects do not throw the S-shaped
behavior into question.
␮m͒ and the formation of a second PSC almost coincides
with the transition to the normal state.
In conclusion, we have developed a simple method to
electrically contact single nanowires such as Pb and Sn. This
technique allows us to probe the nonequilibrium properties
of such 1D superconductors and in particular to observe the
formation of PSCs at temperatures much below the critical
temperature. Moreover, we observed an unusual behavior
when a voltage is applied to such nanowires, which still re-
quires theoretical explanation.
Interesting features were observed when measuring in
the opposite way, that is, applying the voltage and measuring
the current. Here, the current flowing into the nanowire was
determined by measuring the voltage across a 1-⍀ resistance
added in series, and the voltage developed across the sample
was measured separately. In this voltage-driven experiment,
an interesting S-shaped behavior occurs at low temperature
in the formation region of these PSCs, both for the Pb and
the Sn nanowires ͓see Figs. 3͑a͒ and 3͑b͔͒. Although there
We thank the ‘‘Laboratoire des Hauts Polym e` res’’ of the
UCL for providing the polycarbonate membrane samples
used in this study. One of the authors ͑S. M.͒ is a Research
Fellow of the National Fund for Scientific Research ͑FNRS͒
Belgium. This work has been partly supported by the Belgian
Interuniversity Attraction Pole Program ͑PAI-IUAP P5/1/1͒
and by the ‘‘Communaut e´ Fran c¸ aise de Belgique’’ through
the Program ‘‘Actions de Recherches Concert e´ es.’’
have been some theoretical predictions showing such
S-shaped behavior,11 a detailed understanding of this behav-
ior is still lacking. Therefore, we are restricted to pointing
out some interesting experimental observations, at the lowest
measured temperatures ͑i.e., at 1.7 and 4.3 K for Pb and 1.55
K for Sn͒, where the nature of the contact ͑normal in this
case͒ becomes unimportant due to the Andreev reflection
1
2
process. At the first maximum in current, the voltage ob-
tained by subtracting the linear I–V part due to the residual
resistance from the measured one ͑see Fig. 3͒ corresponds
closely to the value of the gap ⌬ ͑Ϸ1.35 mV for Pb and
Ϸ0.56 mV for Sn͒. This tends to indicate that in this voltage-
driven experiment, Cooper pairs are sped up until they reach
the depairing velocity v ϭ⌬/(បk ). The nanowire then
reached progressively, through the negative differential resis-
tance branch of the curve, the state corresponding to the
PSC-like one in the current-driven experiment.
It should be noted that heating effects are unavoidable in
such experiments. Indeed, the heat produced by Joule heat-
ing in the PSC has to be evacuated mostly through the media
surrounding the measured nanowire. Although the thermal
conductivity of polycarbonate is rather low, the surrounding
media is, in fact, a composite material consisting not only of
the polymer medium, but also of metal nanowires, due to the
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